Factor completely. 81-4x^(2)=

Determine the approach: Determine the approach to factor 81 - 4x^2. We can recognize this expression as a difference of squares because it is in the form a^2 - b^2, where both 81 and 4x^2 are perfect squares. 81 = 9^2 and 4x^2 = (2x)^2.Write as a difference of squares: Write 81 - 4x^2 as a difference of squares. 81 - 4x^2 can be written as (9)^2 - (2x)^2.Apply the difference of squares formula: Apply the difference of squares formula. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Using this formula, we can factor (9)^2 - (2x)^2 as (9 - 2x)(9 + 2x).

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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81-4x^{2}=

Determine the approach: Determine the approach to factor $81 - 4x^2$ . $\newline$ We can recognize this expression as a difference of squares because it is in the form $a^2 - b^2$ , where both $81$ and $4x^2$ are perfect squares. $\newline$ $81 = 9^2$ and $4x^2 = (2x)^2$ .
Write as a difference of squares: Write $81 - 4x^2$ as a difference of squares. $\newline$ $81 - 4x^2$ can be written as $(9)^2 - (2x)^2$ .
Apply the difference of squares formula: Apply the difference of squares formula. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ Using this formula, we can factor $(9)^2 - (2x)^2$ as $(9 - 2x)(9 + 2x)$ .