Factor completely. 16x^(2)-81=

Determine Factorization Method: Determine if the expression 16x^2 - 81 can be factored using a known method. The expression is a difference of squares because it can be written as (4x)^2 - 9^2, which fits the pattern a^2 - b^2.Write in a^2 - b^2 Form: Write the expression in the form of a^2 - b^2. 16x^2 = (4x)^2 81 = 9^2 So, 16x^2 - 81 = (4x)^2 - 9^2Apply Difference of Squares Formula: Apply the difference of squares formula, which is a^2 - b^2 = (a - b)(a + b). (4x)^2 - 9^2 = (4x - 9)(4x + 9)Write Final Factored Form: Write the final factored form of the expression. The factored form of 16x^2 - 81 is (4x - 9)(4x + 9).

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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16x^{2}-81

Determine Factorization Method: Determine if the expression $16x^2 - 81$ can be factored using a known method. $\newline$ The expression is a difference of squares because it can be written as $(4x)^2 - 9^2$ , which fits the pattern $a^2 - b^2$ .
Write in $a^2 - b^2$ Form: Write the expression in the form of $a^2 - b^2$ . $\newline$ $16x^2 = (4x)^2$ $\newline$ $81 = 9^2$ $\newline$ So, $16x^2 - 81 = (4x)^2 - 9^2$
Apply Difference of Squares Formula: Apply the difference of squares formula, which is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ $(4x)^2 - 9^2 = (4x - 9)(4x + 9)$
Write Final Factored Form: Write the final factored form of the expression. $\newline$ The factored form of $16x^2 - 81$ is $(4x - 9)(4x + 9)$ .