QuestionFactor completely. $64 x^{2}-16$ $8\left(8 x^{2}-2\right)$ $16(2 x+1)(2 x-1)$ $4(4 x+2)(4 x-2)$ $8(8 x+2)(8 x-2)$

Studdy Solution

STEP 1

1. The expression $64x^2 - 16$ is a difference of squares.
2. The expression can be factored completely using algebraic identities.

STEP 2

1. Identify the difference of squares in the expression.
2. Apply the difference of squares formula.
3. Simplify the expression further if possible.

STEP 3

Recognize that the expression $64x^2 - 16$ is a difference of squares. The general form of a difference of squares is $a^2 - b^2$ , which factors to $(a - b)(a + b)$ .
$64x^2 = (8x)^2 \quad \text{and} \quad 16 = (4)^2$
Thus, the expression can be rewritten as:
$(8x)^2 - (4)^2$

STEP 4

Apply the difference of squares formula:
$(8x - 4)(8x + 4)$

STEP 5

Factor out the greatest common factor from each binomial:
From $8x - 4$ , factor out 4:
$4(2x - 1)$
From $8x + 4$ , factor out 4:
$4(2x + 1)$
Thus, the expression becomes:
$4(2x - 1) \times 4(2x + 1) = 16(2x - 1)(2x + 1)$
The completely factored form of the expression is:
$\boxed{16(2x - 1)(2x + 1)}$

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