Factor the expression completely. 70 x-40x^(4) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. The terms are 70x and 40x^4. The GCF of the numerical coefficients (70 and 40) is 10. Both terms also have an x term, so the GCF is 10x.Factor out GCF: Factor out the GCF from the expression. We can write the expression as 10x(7 - 4x^3).Check for further factoring: Check if the remaining expression inside the parentheses can be factored further. The expression inside the parentheses is 7 - 4x^3, which is a difference of two cubes since 7 is 2^3 and 4x^3 is (2x)^3.Factor difference of cubes: Factor the difference of two cubes using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2). Here, a is 2 and b is 2x, so we get (2 - 2x)(2^2 + 2*2x + (2x)^2).Simplify factored form: Simplify the factored form of the difference of two cubes. We get (2 - 2x)(4 + 4x + 4x^2).Combine with GCF: Combine the GCF factored out earlier with the factored form of the difference of two cubes. The completely factored expression is 10x(2 - 2x)(4 + 4x + 4x^2).Check for further simplification: Check for any further simplification or common factors in the factored terms. There are no further common factors, and the expression is fully simplified.

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Factor the expression completely.

70 x-40x^(4)
Answer:

Factor the expression completely. $\newline$ $70 x-40 x^{4}$ $\newline$ Answer:

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Algebra 1

Evaluate integers raised to rational exponents

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Q. Factor the expression completely.

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70 x-40 x^{4}

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. $\newline$ The terms are $70x$ and $40x^4$ . The GCF of the numerical coefficients ( $70$ and $40$ ) is $10$ . Both terms also have an $x$ term, so the GCF is $10x$ .
Factor out GCF: Factor out the GCF from the expression. $\newline$ We can write the expression as $10x(7 - 4x^3)$ .
Check for further factoring: Check if the remaining expression inside the parentheses can be factored further. $\newline$ The expression inside the parentheses is $7 - 4x^3$ , which is a difference of two cubes since $7$ is $2^3$ and $4x^3$ is $(2x)^3$ .
Factor difference of cubes: Factor the difference of two cubes using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ . Here, $a$ is $2$ and $b$ is $2x$ , so we get $(2 - 2x)(2^2 + 2\cdot2x + (2x)^2)$ .
Simplify factored form: Simplify the factored form of the difference of two cubes. $\newline$ We get $(2 - 2x)(4 + 4x + 4x^2)$ .
Combine with GCF: Combine the GCF factored out earlier with the factored form of the difference of two cubes. $\newline$ The completely factored expression is $10x(2 - 2x)(4 + 4x + 4x^2)$ .
Check for further simplification: Check for any further simplification or common factors in the factored terms. $\newline$ There are no further common factors, and the expression is fully simplified.