Chapter 4.2, Problem 53PS

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# Give a step-by step description of how to do the following multiplication problem. x 2 + 5 x + 6 x 2 − 2 x − 8 ⋅ x 2 − 16 16 − x 2

To determine

To Give:

The step-by-step description for the given multiplication problem.

Explanation

The given multiplication problem is x2+5x+6x2âˆ’2xâˆ’8â‹…x2âˆ’1616âˆ’x2.

Factorised each term by using middle term splitting and formula [a2âˆ’b2=(aâˆ’b)(a+b)].

x2+5x+6x2âˆ’2xâˆ’8â‹…x2âˆ’1616âˆ’x2=x2+3x+2x+6x2âˆ’4x+2xâˆ’8â‹…x2âˆ’(4)2(4)2âˆ’x2=x(x+3)+2(x+3)x(xâˆ’4)+2(xâˆ’4)â‹…(xâˆ’4)(x+4)(4âˆ’x)(4+x)=(x+2)(x+3)(x+2)(xâˆ’4)â‹…(xâˆ’4)(x+4)(4âˆ’x)(4+x)

Cancel the same terms in numerator to denominator

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