Q 269 In the following exercises, fact... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q 269 (page 613)

In the following exercises, factor completely.
$9 x^{2} - 6 x y + y^{2} - 49$

Short Answer

Expert verified

The expression is factored as $9 x^{2} - 6 x y + y^{2} - 49 = (3 x - y - 7) (3 x - y + 7)$

Step by step solution

Step 1. Given Information

Consider the expression $9 x^{2} - 6 x y + y^{2} - 49$ .

The objective is to factor the expression completely.

Step 2. Factor using perfect square trinomial

The trinomial $a^{2} - 2 a b + b^{2}$ is a perfect square trinomial and it is factored as ${(a - b)}^{2}$ .

In the given expression, the first three terms form a perfect square trinomial and so it can be factored as

$\begin{array}{rcl} 9 x^{2} - 6 x y + y^{2} - 49 & = & {(3 x)}^{2} - 2 路 2 x 路 y + {(y)}^{2} - 49 \\ = & {(3 x - y)}^{2} - 49 \end{array}$

Step 3. Factor using the difference of square

The difference of squares can be factored as $a^{2} - b^{2} = (a - b) (a + b)$

Now the first term is a perfect square and the second term $49$ is the square of $7$ . So it can be further factored as

role="math" localid="1644656641651" $\begin{array}{rcl} {(3 x - y)}^{2} - 49 & = & {(3 x - y)}^{2} - 7^{2} \\ = & (3 x - y - 7) (3 x - y + 7) \end{array}$

Step 4. Check the factors

Multiply the factors to check the solution

\begin{array}{rcl} (3 x - y - 7) (3 x - y + 7) & = & 9 x^{2} - 3 x y + 21 x - 3 x y + y^{2} - 7 y - 21 x + 7 y - 49 \\ = & 9 x^{2} - 6 x y + y^{2} - 49 \end{array}

And we get the given expression. So the expression is correctly factored.

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91影视

In the following exercises, factor completely.
$9 x^{2} - 6 x y + y^{2} - 49$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor using perfect square trinomial

Step 3. Factor using the difference of square

Step 4. Check the factors

One App. One Place for Learning.

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91影视

In the following exercises, factor completely.9x2-6xy+y2-49

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor using perfect square trinomial

Step 3. Factor using the difference of square

Step 4. Check the factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely.
$9 x^{2} - 6 x y + y^{2} - 49$