Factor as the product of two binomials. x^(2)-16=

Recognize Quadratic Expression: Recognize the quadratic expression as a difference of squares. The quadratic expression x^2 - 16 can be written as x^2 - 4^2, which is a difference of squares since both x and 4 are squared.Apply Difference of Squares Formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a + b)(a - b). Here, a is x and b is 4.Write as Product of Binomials: Write the expression as the product of two binomials using the formula. Using the formula from Step 2, we have (x + 4)(x - 4).Check Result by Expanding: Check the result by expanding the binomials. To ensure there are no math errors, we can multiply the binomials to see if we get the original expression: (x + 4)(x - 4) = x^2 - 4x + 4x - 16 = x^2 - 16. The middle terms cancel each other out, and we are left with the original expression, confirming that the factorization is correct.

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Algebra 1

Factor quadratics: special cases

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Q. Factor as the product of two binomials.

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x^{2}-16=

Recognize Quadratic Expression: Recognize the quadratic expression as a difference of squares. The quadratic expression $x^2 - 16$ can be written as $x^2 - 4^2$ , which is a difference of squares since both $x$ and $4$ are squared.
Apply Difference of Squares Formula: Apply the difference of squares formula. The difference of squares formula is $a^2 - b^2 = (a + b)(a - b)$ . Here, $a$ is $x$ and $b$ is $4$ .
Write as Product of Binomials: Write the expression as the product of two binomials using the formula. $\newline$ Using the formula from Step $2$ , we have $(x + 4)(x - 4)$ .
Check Result by Expanding: Check the result by expanding the binomials. $\newline$ To ensure there are no math errors, we can multiply the binomials to see if we get the original expression: $\newline$ $(x + 4)(x - 4) = x^2 - 4x + 4x - 16 = x^2 - 16$ . $\newline$ The middle terms cancel each other out, and we are left with the original expression, confirming that the factorization is correct.