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Factor as the product of two binomials.

36-x^(2)=

Factor as the product of two binomials. $\newline$ $36-x^{2}=$

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Factor quadratics: special cases

Full solution

Q. Factor as the product of two binomials.

\newline

36-x^{2}=

Identify factoring type: Identify the type of factoring required for the expression $36 - x^2$ . $\newline$ The expression is a difference of squares, which can be factored using the formula $a^2 - b^2 = (a - b)(a + b)$ .
Recognize difference of squares: Recognize the expression $36 - x^2$ as a difference of squares. $\newline$ $36 = 6 \times 6 = 6^2$ $\newline$ $x^2 = x \times x = (x)^2$ $\newline$ So, $36 - x^2 = 6^2 - x^2$
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $a^2 - b^2 = (a - b)(a + b)$ , we get: $\newline$ $6^2 - x^2 = (6 - x)(6 + x)$
Write final factored form: Write the final factored form of the expression. $\newline$ The factored form of $36 - x^2$ is $(6 - x)(6 + x)$ .

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