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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q 179 (page 603)

In the following exercises, factor completely using the difference of squares pattern, if possible.
$6 p^{2} q^{2} - 54 p^{2}$

Short Answer

Expert verified

The complete factor of trinomial is $6 p^{2} (q - 3) (q + 3)$ .

Step by step solution

01

Step 1. Given information

Consider the given trinomial.

$6 p^{2} q^{2} - 54 p^{2}$

02

Step 2. Formula used

$a^{2} - b^{2} = (a + b) (a - b)$

03

Step 3. Find the factor using difference of square pattern.

$6 p^{2} q^{2} - 54 p^{2} = 6 p^{2} (q^{2} - 9) = 6 p^{2} [{(q)}^{2} - {(3)}^{2}]$

04

Step 4. Write the trinomial as product of conjugate.

$6 p^{2} [(q^{2}) - {(3)}^{2}] = 6 p^{2} (q - 3) (q + 3)$

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Most popular questions from this chapter

In the following exercises, factor each trinomial of the form $x^{2} - b x + c$ .

$5 p - 6 + p^{2}$

Factor completely using trial and error: $10 y^{2} - 37 y + 7$

In the following exercises, factor completely.

$48 q^{3} - 24 q^{2} + 3 q$

Factor by Grouping In the following exercises, factor by grouping.

$u^{2} - u + 6 u - 6$

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .

u^{2} + 101 u + 100

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