Answer 4 ( a + 3 ) 3 a 2 Explanation Given: Expression: 8 a 2 − 3 a ⋅ a 2 − 9 6 a Concept used: To simplify the given expression: Find the Least Common Multiple of the fraction and write in reduced form. Take out common terms in the given expression. Cancel out the terms that are in common in numerator and the denominator. Find if any algebraic identities can simplify the given expression. Formula used: ( a 2 − b 2 ) = ( a + b ) ( a − b ) Calculation: Using the above concept, ⇒ 8 a 2 − 3 a ⋅ a 2 − 9 6 a ⇒ 8 ( a 2 − 9 ) 6 a ( a 2 − 3 a ) Take out the common terms in the numerator and denominator. ⇒ 8 ( a 2 − 9 ) 6 a ( a 2 − 3 a ) ⇒ 8 ( a − 3 ) ( a + 3 ) 6 a a ( a − 3 ) [ ∵ ( a 2 − b 2 ) = ( a + b ) ( a − b ) ] ⇒ 8 ( a + 3 ) 6 a 2 ⇒ 4 ( a + 3 ) 3 a 2 Conclusion: Therefore, the simplified form of the expression is 4 ( a + 3 ) 3 a 2 .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.7, Problem 2MRE

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 2MRE

4(a+3)3a2

Explanation of Solution

Given:

Expression: 8a2−3a⋅a2−96a

Concept used:

To simplify the given expression:

Find the Least Common Multiple of the fraction and write in reduced form.
Take out common terms in the given expression.
Cancel out the terms that are in common in numerator and the denominator.
Find if any algebraic identities can simplify the given expression.

Formula used:

(a2−b2)=(a+b)(a−b)

Calculation:

Using the above concept,

⇒8a2−3a⋅a2−96a⇒8(a2−9)6a(a2−3a)

Take out the common terms in the numerator and denominator.

⇒8(a2−9)6a(a2−3a)⇒8(a−3)(a+3)6aa(a−3) [∵(a2−b2)=(a+b)(a−b)]⇒8(a+3)6a2⇒4(a+3)3a2

Conclusion:

Therefore, the simplified form of the expression is 4(a+3)3a2.

Chapter 5.7, Problem 1MRE

Chapter 5.7, Problem 3MRE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

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