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Chapter 6: Q. 192 (page 603)

In the following exercises, factor completely using the difference of squares pattern, if possible.

p2+14p+49-q2

Short Answer

Expert verified

The factored form of the given expression is (p+7-q)(p+7+q).

Step by step solution

01

Step 1. Given information.

The given expression is:
p2+14p+49-q2

02

Step 2. Determine the factored form.

The given expression can be written as:
p2+14p+49-q2=(p2+2(p)(7)+72)-q2=(p+7)2-q2鈭�(a+b)2=a2+2ab+b2=(p+7-q)(p+7+q)鈭�a2-b2=(a-b)(a+b)

03

Step 3. Conclusion.

The factored form of the given expression is(p+7-q)(p+7+q).

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