Chapter 6: Q. 192 (page 603)

In the following exercises, factor completely using the difference of squares pattern, if possible.
$p^{2} + 14 p + 49 - q^{2}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

The given expression is:
$p^{2} + 14 p + 49 - q^{2}$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl} p^{2} + 14 p + 49 - q^{2} & = & (p^{2} + 2 (p) (7) + 7^{2}) - q^{2} \\ = & {(p + 7)}^{2} - q^{2} [∵ {(a + b)}^{2} = a^{2} + 2 a b + b^{2}] \\ = & (p + 7 - q) (p + 7 + q) [∵ {a^{2} - b}^{2} = (a - b) (a + b)] \end{array}$

Step 3. Conclusion.

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

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In the following exercises, factor completely using the difference of squares pattern, if possible.
$p^{2} + 14 p + 49 - q^{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the factored form.

Step 3. Conclusion.

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In the following exercises, factor completely using the difference of squares pattern, if possible.p2+14p+49-q2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the factored form.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Geometry

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the difference of squares pattern, if possible.
$p^{2} + 14 p + 49 - q^{2}$