Chapter 7: Q. 102 (page 832)

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$p^{2} - 16 p q + 63 q^{2}$

Short Answer

Expert verified

The factorization of $p^{2} - 16 p q + 63 q^{2}$ is $(p - 7 q) (p - 9 q)$

Step by step solution

Step 1. Given information

Given expression is $p^{2} - 16 p q + 63 q^{2}$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

The factors of 63	Sum of factors
9, 7	9 + 7 = 16
21, 3	21 + 3 = 24
-7, -9	-7+ (-9) = -16
-21, -3	-21 + (-3) = -24

Step 3. Factorization

Use $- 7$ and $- 9$ as the last terms of the trinomials.

$p^{2} - 16 p q + 63 q^{2} = (p - 7 q) (p - 9 q)$

Step 4. Check

$(p - 7 q) (p - 9 q) = p^{2} - 7 p q - 9 p q + 63 q^{2} = p^{2} - 16 p q + 63 q^{2}$

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In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$p^{2} - 16 p q + 63 q^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials.

Step 3. Factorization

Step 4. Check

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In the following exercises, factor each trinomial of the form x2+bxy+cy2p2-16pq+63q2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials.

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Calculus

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$p^{2} - 16 p q + 63 q^{2}$