Factor completely: 1-8x^(3) Answer:

Recognize Cubic Expression: Recognize the expression 1 - 8x^3 as a difference of cubes. A difference of cubes can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2). Here, 1 can be written as 1^3 and 8x^3 can be written as (2x)^3.Apply Difference of Cubes Formula: Apply the difference of cubes formula. Let a = 1 and b = 2x. The factored form will be (1 - 2x)(1^2 + 1*2x + (2x)^2).Simplify Factored Form: Simplify the factored form. Simplify the second term (1^2 + 1*2x + (2x)^2) to (1 + 2x + 4x^2). The fully factored form is (1 - 2x)(1 + 2x + 4x^2).

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Q. Factor completely:

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1-8 x^{3}

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Answer:

Recognize Cubic Expression: Recognize the expression $1 - 8x^3$ as a difference of cubes. $\newline$ A difference of cubes can be factored using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ . $\newline$ Here, $1$ can be written as $1^3$ and $8x^3$ can be written as $(2x)^3$ .
Apply Difference of Cubes Formula: Apply the difference of cubes formula. $\newline$ Let $a = 1$ and $b = 2x$ . $\newline$ The factored form will be $(1 - 2x)(1^2 + 1\cdot2x + (2x)^2)$ .
Simplify Factored Form: Simplify the factored form. $\newline$ Simplify the second term $(1^2 + 1\cdot2x + (2x)^2)$ to $(1 + 2x + 4x^2)$ . $\newline$ The fully factored form is $(1 - 2x)(1 + 2x + 4x^2)$ .