Chapter 47, Problem 4AR

To determine

(a)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $13P$.

Explanation of Solution

Given information:

  $-8P+21P$

Calculation:

The given expression to simplify is $-8P+21P$.

  $\begin{array}{l}\text{{Applying the addition rule in a given problem}}\\ \Rightarrow -8P+21P\\ \Rightarrow 13P\end{array}$

To determine

(b)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-1.18{\text{H}}^2$

Explanation of Solution

Given information:

  $-0.05{\text{H}}^2-1.13H^2$

Calculation:

The given expression to simplify is $-0.05{\text{H}}^2-1.13H^2$.

  $\begin{array}{l}\text{{Applying the addition rule in a given problem}}\\ \Rightarrow -0.05{\text{H}}^2-1.13H^2\\ \Rightarrow -1.18{\text{H}}^2\end{array}$

To determine

(c)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $5d+22d^2$.

Explanation of Solution

Given information:

  $12d+8d^2-7d+14d^2$

Calculation:

The given expression to simplify is $12d+8d^2-7d+14d^2$.

  $\begin{array}{l}\text{{Applying the addition rule in a given problem}}\\ \Rightarrow 12d+8d^2-7d+14d^2\\ \Rightarrow 5d+22d^2\end{array}$

To determine

(d)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-a+2a^2$.

Explanation of Solution

Given information:

  $(5a-2a^2)-\left(6a-4a^2\right)$

Calculation:

The given expression to simplify is $(5a-2a^2)-\left(6a-4a^2\right)$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow (5a-2a^2)-\left(6a-4a^2\right)\\ \Rightarrow 5a-2a^2-6a+4a^2\\ \Rightarrow (5-6)a+a^2(-2+4)\\ \Rightarrow -a+2a^2\end{array}$

To determine

(e)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-90x^{3}y$.

Explanation of Solution

Given information:

  $(-10x)(9x^{2}y)$

Calculation:

The given expression to simplify is $(-10x)(9x^{2}y)$.

  $\begin{array}{l}\text{{Applying the multiplication rule in a given problem}}\\ \Rightarrow (-10x)(9x^{2}y)\\ \Rightarrow -90x^{3}y\end{array}$

To determine

(f)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-5.9e^2{f}^4$.

Explanation of Solution

Given information:

  $(-5.9e^2{f}^2)(-f^2)$

Calculation:

The given expression to simplify is $(-5.9e^2{f}^2)(-f^2)$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow (-5.9e^2{f}^2)(-f^2)\\ \Rightarrow -5.9e^2{f}^4\end{array}$

To determine

(g)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $32x-8x^2$.

Explanation of Solution

Given information:

  $(16x^2-4x^3)÷\left(0.5x\right)$

Calculation:

The given expression to simplify is $(16x^2-4x^3)÷\left(0.5x\right)$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow (16x^2-4x^3)÷\left(0.5x\right)\\ \Rightarrow \frac{16x}{0.5}-\frac{4x^2}{0.5}\\ \Rightarrow 32x-8x^2\end{array}$

To determine

(h)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $3f{g}^3-5g-10f$.

Explanation of Solution

Given information:

  $(0.6f^2{g}^3-fg-2f^2)÷0.2f$

Calculation:

The given expression to simplify is $(0.6f^2{g}^3-fg-2f^2)÷0.2f$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow (0.6f^2{g}^3-fg-2f^2)÷0.2f\\ \Rightarrow 3f{g}^3-5g-10f\end{array}$

To determine

(i)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-18x^5+6x^2{y}^2+3x^3{y}^3-y^5$.

Explanation of Solution

Given information:

  $(6x^2-y^3)(-3x^3+y^2)$

Calculation:

The given expression to simplify is $(6x^2-y^3)(-3x^3+y^2)$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow (6x^2-y^3)(-3x^3+y^2)\\ =6x^2(-3x^3+y^2)-y^3(-3x^3+y^2)\\ =-18x^5+6x^2{y}^2+3x^3{y}^3-y^5\end{array}$

To determine

(j)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-64a^9{b}^3{c}^6$.

Explanation of Solution

Given information:

  ${(-4a^{3}b{c}^2)}^3$

Calculation:

The given expression to simplify is ${(-4a^{3}b{c}^2)}^3$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ $ \Rightarrow {(-4a^{3}b{c}^2)}^3$\Rightarrow -64a^9{b}^3{c}^6\end{array}$

To determine

(k)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $x^6{y}^{12}-2x^5{y}^8+x^4{y}^4$.

Explanation of Solution

Given information:

  ${[{(x{y}^2)}^3-(x^2{y}^2)]}^2$

Calculation:

The given expression to simplify is ${[{(x{y}^2)}^3-(x^2{y}^2)]}^2$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ $ \Rightarrow {[{(x{y}^2)}^3-(x^2{y}^2)]}^2$$ \Rightarrow {(x^3{y}^6)}^2-2(x^3{y}^6)(x^2{y}^2)+{(x^2{y}^2)}^2$\Rightarrow x^6{y}^{12}-2x^5{y}^8+x^4{y}^4\end{array}$

To determine

(l)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-3a^{2}b{c}^{{}^3}$.

Explanation of Solution

Given information:

  $\left(\sqrt[3]{-27a^6{b}^3{c}^9}\right)$

Calculation:

The given expression to simplify is $\left(\sqrt[3]{-27a^6{b}^3{c}^9}\right)$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow \left(\sqrt[3]{-27a^6{b}^3{c}^9}\right)\\ \Rightarrow -3a^{2}b{c}^{{}^3}\end{array}$

To determine

(m)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $\frac{5e^{2}g{d}^{\frac{1}{2}}}{8}$.

Explanation of Solution

Given information:

  $\sqrt[3]{\frac{25e^4{g}^{2}d}{64}}$

Calculation:

The given expression to simplify is $\sqrt[3]{\frac{25e^4{g}^{2}d}{64}}$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow \sqrt[3]{\frac{25e^4{g}^{2}d}{64}}\\ \Rightarrow \frac{5e^{2}g{d}^{\frac{1}{2}}}{8}\end{array}$

To determine

(n)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-6x^2-6y+12x$.

Explanation of Solution

Given information:

  $-6\left(x^2+y-2x\right)$

Calculation:

The given expression to simplify is $-6\left(x^2+y-2x\right)$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow -6\left(x^2+y-2x\right)\\ \Rightarrow -6x^2-6y+12x\end{array}$

To determine

(o)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $24-m$.

Explanation of Solution

Given information:

  $36-(m^2+m)+(m^3-12)$

Calculation:

The given expression to simplify is $36-(m^2+m)+(m^3-12)$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ \Rightarrow 36-(m^2+m)+(m^3-12)\\ \Rightarrow 36-m^3+m^3-m-12\\ \Rightarrow 36-12-m\\ \Rightarrow 24-m\end{array}$

To determine

(p)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $-12a^3+6a^2$.

Explanation of Solution

Given information:

  $-3a{(2a)}^2+\sqrt{36a^2}$

Calculation:

The given expression to simplify is $-3a{(2a)}^2+\sqrt{36a^2}$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ $ \Rightarrow -3a{(2a)}^2+\sqrt{36a^2}$\Rightarrow -3a(4a^2)+6a\\ \Rightarrow -12a^3+6a^2\end{array}$

To determine

(q)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $9y+20x-x^3{y}^2+xy$.

Explanation of Solution

Given information:

  $9y-x[-8+{(xy)}^2-y]+12x$

Calculation:

The given expression to simplify is $9y-x[-8+{(xy)}^2-y]+12x$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ $ \Rightarrow 9y-x[-8+{(xy)}^2-y]+12x$\Rightarrow 9y+8x-x^3{y}^2+xy+12x\\ \Rightarrow 9y+20x-x^3{y}^2+xy\end{array}$

To determine

(r)

The simplified form of the given expression be performing the indicated operations.

Answer to Problem 4AR

  $28b^{2}m$.

Explanation of Solution

Given information:

  $b{(b+7m)}^2-b{(b-7m)}^2$

Calculation:

The given expression to simplify is $b{(b+7m)}^2-b{(b-7m)}^2$.

  $\begin{array}{l}\text{{Applying the algebric rule in a given problem}}\\ $ \Rightarrow b{(b+7m)}^2-b{(b-7m)}^2$\Rightarrow b(b+7m)(b+7m)-b(b-7m)(b-7m)\\ \Rightarrow b^3+2b^2(7m)+49m^2\\ \Rightarrow 28b^{2}m\end{array}$