1 Foundations 2 Solving Linear Equations 3 Graphs And Functions 4 Systems Of Linear Equations 5 Polynomials And Polynomial Functions 6 Factoring 7 Rational Expressions And Functions 8 Roots And Radicals 9 Quadratic Equations And Functions 10 Exponential And Logarithmic Functions 11 Conics 12 Sequences, Series And Binomial Theorem Chapter5: Polynomials And Polynomial Functions
5.1 Add And Subtract Polynomials 5.2 Properties Of Exponents And Scientific Notation 5.3 Multiply Polynomials 5.4 Dividing Polynomials Chapter Questions Section5.3: Multiply Polynomials
Problem 5.49TI: Multiply: (a) (5y7)(7y4) (b) (25a4b3)(15ab3) . Problem 5.50TI: Multiply: (a) (6b4)(9b5) (b) (23r5s)(12r6s7) . Problem 5.51TI: Multiply: (a) 3y(5y2+8y7) (b) 4x2y2(3x25xy+3y2) . Problem 5.52TI: Multiply: (a) 4x2(2x23x+5) (b) 6a3b(3a22ab+6b2) . Problem 5.53TI: Multiply: (a) (x+8)(x+9) (b) (3c+4)(5c2) . Problem 5.54TI: Multiply: (a) (5x+9)(4x+3) (b) (5y+2)(6y3) . Problem 5.55TI: Multiply: (a) (x7)(x+5) (b) (3x+7)(5x2) . Problem 5.56TI: Multiply: (a) (b3)(b+6) (b) (4y+5)(4y10) . Problem 5.57TI: Multiply: (a) (x2+6)(x8) (b) (2ab+5)(4ab4) . Problem 5.58TI: Multiply: (a) (y2+7)(y9) (b) (2xy+3)(4xy5) . Problem 5.59TI: Multiply using the Vertical Method: (5m7)(3m6) . Problem 5.60TI: Multiply using the Vertical Method: (6b5)(7b3) . Problem 5.61TI: Multiply (y3)(y25y+2) using (a) the Distributive Property and (b) the Vertical Method. Problem 5.62TI: Multiply (x+4)(2x23x+5) using (a) the Distributive Property and (b) the Vertical Method. Problem 5.63TI: Multiply: (a) (x+9)2 (b) (2cd)2 . Problem 5.64TI: Multiply: (a) (y+11)2 (b) (4x5y)2 . Problem 5.65TI: Multiply: (a) (6x+5)(6x5) (b) (4p7q)(4p+7q) . Problem 5.66TI: Multiply: (a) (2x+7)(2x7) (b) (3xy)(3x+y) . Problem 5.67TI: Choose the appropriate pattern and use it to find the product: (a) (9b2)(2b+9) (b) (9p4)2 (c)... Problem 5.68TI: Choose the appropriate pattern and use it to find the product: (a) (6x+7)2 (b) (3x4)(3x+4) (c)... Problem 5.69TI: For functions f(x)=x5 and g(x)=x22x+3 , find (a) (fg)(x) (b) (fg)(2) . Problem 5.70TI: For functions f(x7) and g(x)=x2+8x+4 , find (a) (fg)(x) (b) (fg)(2) . Problem 178E: In the following exercises, multiply the monomials. 178. (a) (6y7)(3y4) (b) (47rs2)(14rs3) Problem 179E: In the following exercises, multiply the monomials. 179. (a) (10x5)(3x3) (b) (58x3y)(24x5y) Problem 180E: In the following exercises, multiply the monomials. 180. (a) (8u6)(9u) (b) (23x2y)(34xy2) Problem 181E: In the following exercises, multiply the monomials. 181. (a) (6c4)(12c) (b) (35m3n2)(59m2n3) Problem 182E: In the following exercises, multiply. 182. (a) 8x(x2+2x15) (b) 5pq3(p22pq+6q2) Problem 183E: In the following exercises, multiply. 183. (a) 5t(t2+3t18); (b) 9r3s(r23rs+5s2) Problem 184E: In the following exercises, multiply. 184. (a) 8y(y2+2y15) (b) 4y2z2(3y2+12yzz2) Problem 185E: In the following exercises, multiply. 185. (a) 5m(m2+3m18) (b) 3x2y2(7x2+10xyy2) Problem 186E: In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL... Problem 187E: In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL... Problem 188E: In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL... Problem 189E: In the following exercises, multiply the binomials using (a) the Distributive Property; (b) the FOIL... Problem 190E: In the following exercises, multiply the binomials. Use any method. 190. (x+8)(x+3) Problem 191E: In the following exercises, multiply the binomials. Use any method. 191. (y6)(y2) Problem 192E: In the following exercises, multiply the binomials. Use any method. 192. (2t9)(10t+1) Problem 193E: In the following exercises, multiply the binomials. Use any method. 193. (6p+5)(p+1) Problem 194E: In the following exercises, multiply the binomials. Use any method. 194. (q5)(q+8) Problem 195E: In the following exercises, multiply the binomials. Use any method. 195. (m+11)(m4) Problem 196E: In the following exercises, multiply the binomials. Use any method. 196. (7m+1)(m3) Problem 197E: In the following exercises, multiply the binomials. Use any method. 197. (3r8)(11r+1) Problem 198E: In the following exercises, multiply the binomials. Use any method. 198. (x2+3)(x+2) Problem 199E: In the following exercises, multiply the binomials. Use any method. 199. (y24)(y+3) Problem 200E: In the following exercises, multiply the binomials. Use any method. 200. (5ab1)(2ab+3) Problem 201E: In the following exercises, multiply the binomials. Use any method. 201. (2xy+3)(3xy+2) Problem 202E: In the following exercises, multiply the binomials. Use any method. 202. (x2+8)(x25) Problem 203E: In the following exercises, multiply the binomials. Use any method. 203. (y27)(y24) Problem 204E: In the following exercises, multiply the binomials. Use any method. 204. (6pq3)(4pq5) Problem 205E: In the following exercises, multiply the binomials. Use any method. 205. (3rs7)(3rs4) Problem 206E: In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method.... Problem 207E: In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method.... Problem 208E: In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method.... Problem 209E: In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method.... Problem 210E: In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method.... Problem 211E: In the following exercises, multiply using (a) the Distributive Property; (b) the Vertical Method.... Problem 212E: In the following exercises, multiply. Use either method. 212. (w7)(w29w+10) Problem 213E: In the following exercises, multiply. Use either method. 213. (p4)(p26p+9) Problem 214E: In the following exercises, multiply. Use either method. 214. (3q+1)(q24q5) Problem 215E: In the following exercises, multiply. Use either method. 215. (6r+1)(r27r9) Problem 216E: In the following exercises, square each binomial using the Binomial Squares Pattern. 216. (w+4)2 Problem 217E: In the following exercises, square each binomial using the Binomial Squares Pattern. 217. (q+12)2 Problem 218E: In the following exercises, square each binomial using the Binomial Squares Pattern. 218. (3xy)2 Problem 219E: In the following exercises, square each binomial using the Binomial Squares Pattern. 219. (2y3z2) Problem 220E: In the following exercises, square each binomial using the Binomial Squares Pattern. 220. (y+14)2 Problem 221E: In the following exercises, square each binomial using the Binomial Squares Pattern. 221. (x+23)2 Problem 222E: In the following exercises, square each binomial using the Binomial Squares Pattern. 222. (15x17y)2 Problem 223E: In the following exercises, square each binomial using the Binomial Squares Pattern. 223. (18x19y)2 Problem 224E: In the following exercises, square each binomial using the Binomial Squares Pattern. 224. (3x2+2)2 Problem 225E: In the following exercises, square each binomial using the Binomial Squares Pattern. 225. (5u2+9)2 Problem 226E: In the following exercises, square each binomial using the Binomial Squares Pattern. 226. (4y32)2 Problem 227E: In the following exercises, square each binomial using the Binomial Squares Pattern. 227. (8p33)2 Problem 228E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 229E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 230E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 231E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 232E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 233E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 234E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 235E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 236E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 237E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 238E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 239E: In the following exercises, multiply each pair of conjugates using the Product of Conjugates... Problem 240E: In the following exercises, find each product. 240. (p3)(p+3) Problem 241E: In the following exercises, find each product. 241. (t9)2 Problem 242E: In the following exercises, find each product. 242. (m+n)2 Problem 243E: In the following exercises, find each product. 243. (2x+y)(x2y) Problem 244E: In the following exercises, find each product. 244. (2r+12)2 Problem 245E: In the following exercises, find each product. 245. (3p+8)(3p8) Problem 246E: In the following exercises, find each product. 246. (7a+b)(a7b) Problem 247E: In the following exercises, find each product. 247. (k6)2 Problem 248E: In the following exercises, find each product. 248. (a57b)2 Problem 249E: In the following exercises, find each product. 249. (x2+8y)(8xy2) Problem 250E: In the following exercises, find each product. 250. (r6+s6)(r6s6) Problem 251E: In the following exercises, find each product. 251. (y4+2z)2 Problem 252E: In the following exercises, find each product. 252. (x5+y5)(x5y5) Problem 253E: In the following exercises, find each product. 253. (m38n)2 Problem 254E: In the following exercises, find each product. 254. (9p+8q)2 Problem 255E: In the following exercises, find each product. 255. (r2s3)(r3+s2) Problem 256E: (10y6)+(4y7) Problem 257E: (15p4)+(3p5) Problem 258E: (x24x34)(x2+7x6) Problem 259E: (j28j27)(j2+2j12) Problem 260E: (15f8)(20f3) Problem 261E: (14d5)(36d2) Problem 262E: (4a3b)(9a2b6) Problem 263E: (6m4n3)(7mn5) Problem 264E: 5m(m2+3m18) Problem 265E: 5q3(q22q+6) Problem 266E: (s7)(s+9) Problem 267E: (y22y)(y+1) Problem 268E: (5xy)(x4) Problem 269E: (6k1)(k2+2k4) Problem 270E: (3x11y)(3x11y) Problem 271E: (11b)(11+b) Problem 272E: (rs27)(rs+27) Problem 273E: (2x23y4)(2x2+3y4) Problem 274E: (m15)2 Problem 275E: (3d+1)2 Problem 276E: (4a+10)2 Problem 277E: (3z+15)2 Problem 278E: For functions f(x)=x+2 and g(x)=3x22x+4 , find (a) (fg)(x) (b) (fg)(1) Problem 279E: For functions f(x)=x1 and g(x)=4x2+3x5 , find (a) (fg)(x) (b) (fg)(2) Problem 280E: For functions f(x)=2x7 and g(x)=2x+7 , find (a) (fg)(x) (b) (fg)(3) Problem 281E: For functions f(x)=7x8 and g(x)=7x+8 , find (a) (fg)(x) (b) (fg)(2) Problem 282E: For functions f(x)=x25x+2 and g(x)=x23x1 , find (a) (fg)(x) (b) (fg)(1) Problem 283E: For functions f(x)=x2+4x3 and g(x)=x2+2x+4 , find (a) (fg)(x) (b) (fg)(1) Problem 284E: Which method do you prefer to use when multiplying two binomials: the Distributive Property or the... Problem 285E: Multiply the following: (x+2)(x2)(y+7)(y7)(w+5)(w5) Explain the pattern that you see in your... Problem 286E: Multiply the following: (p+3)(p+3)(q+6)(q+6)(r+1)(r+1) Explain the pattern that you see in your... Problem 287E: Why does (a+b)2 result in a trinomial, but (ab)(a+b) result in a binomial? Problem 5.64TI: Multiply: (a) (y+11)2 (b) (4x5y)2 .
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Use an iterated integral to calculate the area of the region shown in the following figure.
Transcribed Image Text: P+ y² = 1
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x + y = 1
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With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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