Factor completely. 25-x^(2) Answer:

Identify as difference of squares: Identify the expression 25 - x^2 as a difference of squares. The expression can be written as a^2 - b^2, where a^2 = 25 and b^2 = x^2. This means a = 5 and b = x, since 5^2 = 25 and x^2 = x^2.Apply formula to factor: Apply the difference of squares formula to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Substitute a = 5 and b = x into the formula to get (5 - x)(5 + x).Write final factored form: Write the final factored form of the expression. The factored form of 25 - x^2 is (5 - x)(5 + x).

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Algebra 1

Factor quadratics: special cases

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Q. Factor completely.

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25-x^{2}

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Answer:

Identify as difference of squares: Identify the expression $25 - x^2$ as a difference of squares. $\newline$ The expression can be written as $a^2 - b^2$ , where $a^2 = 25$ and $b^2 = x^2$ . $\newline$ This means $a = 5$ and $b = x$ , since $5^2 = 25$ and $x^2 = x^2$ .
Apply formula to factor: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Substitute $a = 5$ and $b = x$ into the formula to get $(5 - x)(5 + x)$ .
Write final factored form: Write the final factored form of the expression. $\newline$ The factored form of $25 - x^2$ is $(5 - x)(5 + x)$ .