Identify Common Factor: Identify the common factor in both terms of the expression x^3 - 81x. Both terms have an x in common, so we can factor out an x.Factor Out 'x': Factor out the common x from the expression. x^3 - 81x can be factored as x(x^2 - 81).Recognize Difference of Squares: Recognize that the expression inside the parentheses is a difference of squares. x^2 - 81 can be factored further because it is a difference of squares (a^2 - b^2), where a = x and b = 9.Factor Difference of Squares: Factor the difference of squares. x^2 - 81 factors into (x + 9)(x - 9).Write Fully Factored Form: Write the fully factored form of the original expression. The factored form of x^3 - 81x is x(x + 9)(x - 9).

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$x^{3}-81 x$

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Math Problems

Grade 8

Multiply powers: integer bases

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x^{3}-81 x

Identify Common Factor: Identify the common factor in both terms of the expression $x^3 - 81x$ . Both terms have an $x$ in common, so we can factor out an $x$ .
Factor Out 'x': Factor out the common x from the expression. $\newline$ $x^3 - 81x$ can be factored as $x(x^2 - 81)$ .
Recognize Difference of Squares: Recognize that the expression inside the parentheses is a difference of squares. $x^2 - 81$ can be factored further because it is a difference of squares $(a^2 - b^2)$ , where $a = x$ and $b = 9$ .
Factor Difference of Squares: Factor the difference of squares. $x^2 - 81$ factors into $(x + 9)(x - 9)$ .
Write Fully Factored Form: Write the fully factored form of the original expression. $\newline$ The factored form of $x^3 - 81x$ is $x(x + 9)(x - 9)$ .