Question #c5cab

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Question #c5cab

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Answer 1 · 2017-09-04T16:22:52

$(a + 3 a b + 2 b) (a - 3 a b)$ $(a+3ab+2b)(a-3ab)$

Explanation:

${(a + b)}^{2} - {(3 a b + b)}^{2}$ $(a+b)^2-(3ab+b)^2$

Recall the general difference of squares factorization technique: $x^{2} - y^{2} = (x + y) (x - y)$ $color(red)x^2-color(blue)y^2=(color(red)x+color(blue)y)(color(red)x-color(blue)y)$ .

Thus:

${(a + b)}^{2} - {(3 a b + b)}^{2} = (a + b + 3 a b + b) (a + b - (3 a b + b))$ $color(red)((a+b))^2-color(blue)((3ab+b))^2=(color(red)(a+b)+color(blue)(3ab+b))(color(red)(a+b)-color(blue)((3ab+b)))$

Clean up within the parentheses:

$= (a + 3 a b + 2 b) (a - 3 a b)$ $=(a+3ab+2b)(a-3ab)$

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Question #c5cab

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