QuestionFactor $36 x^{2}-49$

Studdy Solution

STEP 1

1. The expression $36x^2 - 49$ is a difference of squares.
2. The difference of squares can be factored using the formula $a^2 - b^2 = (a-b)(a+b)$ .

STEP 2

1. Identify the squares in the expression $36x^2 - 49$ .
2. Apply the difference of squares formula to factor the expression.

STEP 3

Identify the squares in the expression. Recognize that:
$36x^2 = (6x)^2$ $49 = 7^2$
Thus, the expression $36x^2 - 49$ can be rewritten as:
$(6x)^2 - 7^2$

STEP 4

Apply the difference of squares formula $a^2 - b^2 = (a-b)(a+b)$ .
For $(6x)^2 - 7^2$ , let $a = 6x$ and $b = 7$ . Then:
$(6x)^2 - 7^2 = (6x - 7)(6x + 7)$
The factored form of the expression is:
$\boxed{(6x - 7)(6x + 7)}$

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