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Chapter 0: Problem 87

Factor completely, or state that the polynomial is prime. $$9 b^{2} x-16 y-16 x+9 b^{2} y$$

Short Answer

Expert verified
The factored form of the given polynomial is \((x+y)(9b^{2}-16)\).

Step by step solution

01

Identify and regroup like terms

First, rearrange the polynomial by grouping all terms with common factors together. This gives \(9 b^{2} x+9 b^{2} y-16 x-16 y\).
02

Factor out the common terms

Factor out the common terms from each group. From the first two terms, we can factor out \(9b^{2}\), and from the last two terms, we can factor out -16. This results in \(9b^{2}(x+y)-16(x+y)\).
03

Factor out the common binomial

We notice that the polynomial is now in the form of \(a(x+y)-b(x+y)\), where \(a=9b^{2}\), \(b=16\), and \(x+y\) is a common binomial. Therefore, we factor out \(x+y\) to get \((x+y)(9b^{2}-16)\).

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