Factor as the product of two binomials. 25-x^(2)=

Identify the expression: 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.Find the square roots: Find the square roots of a^2 and b^2. The square root of 25 is 5, so a = 5. The square root of x^2 is x, so b = x.Apply the difference of squares formula: Apply the difference of squares formula. The formula for the difference of squares 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 the final factored form: Write the final factored form. The factored form of 25 - x^2 is (5 - x)(5 + x).

Home

Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor as the product of two binomials.

\newline

25-x^{2}=

Identify the expression: 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 $b^2 = x^2$ .
Find the square roots: Find the square roots of $a^2$ and $b^2$ . $\newline$ The square root of $25$ is $5$ , so $a = 5$ . $\newline$ The square root of $x^2$ is $x$ , so $b = x$ .
Apply the difference of squares formula: Apply the difference of squares formula. $\newline$ The formula for the difference of squares 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 the final factored form: Write the final factored form. $\newline$ The factored form of $25 - x^2$ is $(5 - x)(5 + x)$ .