How do you factor by grouping $2x^3 + 4x^2 y - 2x^2 - 4xy$ ?

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How do you factor by grouping $2x^3 + 4x^2 y - 2x^2 - 4xy$ ?

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Answer 1 · 2015-05-04T21:24:34

Notice the similarity of the coefficients, 2, 4, -2, -4. It prompts to group the four terms of this expression into two groups:
Group 1: $2x^3+4x^2y$
Group 2: $-2x^2-4xy$

Factor out $2x^2$ in the first group, getting
$2x^2(x+2y)$
Factor out $-2x$ in the second group, getting
$-2x(x+2y)$

Now you see that $(x+2y)$ is a common factor in both groups. Therefore, the original expression can be represented as:
$2x^2(x+2y)-2x(x+2y)=(2x^2-2x)(x+y)=2x(x-1)(x+2y)$

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How do you factor by grouping $2x^3 + 4x^2 y - 2x^2 - 4xy$ ?

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How do you factor by grouping 2x^3 + 4x^2 y - 2x^2 - 4xy2x^3 + 4x^2 y - 2x^2 - 4xy?

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How do you factor by grouping $2x^3 + 4x^2 y - 2x^2 - 4xy$ ?