Factor completely. 2x^(2)-162=

Identify common factor: Identify if there is a common factor in the terms 2x^2 and -162. Both terms are even, so they have a common factor of 2. Factor out the 2: 2(x^2 - 81)Factor out the common factor: Recognize that x^2 - 81 is a difference of squares. x^2 = x * x = (x)^2 81 = 9 * 9 = 9^2 So, x^2 - 81 = (x)^2 - 9^2Recognize difference of squares: Use the difference of squares formula to factor x^2 - 81. The formula is a^2 - b^2 = (a - b)(a + b). (x)^2 - 9^2 = (x - 9)(x + 9)Use difference of squares formula: Combine the factored form of x^2 - 81 with the common factor 2 that was factored out in Step 1. 2(x^2 - 81) = 2(x - 9)(x + 9)

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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2x^{2}-162

Identify common factor: Identify if there is a common factor in the terms $2x^2$ and $-162$ . $\newline$ Both terms are even, so they have a common factor of $2$ . $\newline$ Factor out the $2$ : $2(x^2 - 81)$
Factor out the common factor: Recognize that $x^2 - 81$ is a difference of squares. $\newline$ $x^2 = x \times x = (x)^2$ $\newline$ $81 = 9 \times 9 = 9^2$ $\newline$ So, $x^2 - 81 = (x)^2 - 9^2$
Recognize difference of squares: Use the difference of squares formula to factor $x^2 - 81$ . $\newline$ The formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ $(x)^2 - 9^2 = (x - 9)(x + 9)$
Use difference of squares formula: Combine the factored form of $x^2 - 81$ with the common factor $2$ that was factored out in Step $1$ . $\newline$ $2(x^2 - 81) = 2(x - 9)(x + 9)$