How do you factor by grouping $4 b^{2} + 4 b c + c^{2} - 16$ $4b^2+4bc+c^2-16$ ?

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How do you factor by grouping $4 b^{2} + 4 b c + c^{2} - 16$ $4b^2+4bc+c^2-16$ ?

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Answer 1 · 2015-06-23T22:41:29

$(2 b + c + 4) \cdot (2 b + c - 4)$ $(2b+c+4)*(2b+c-4)$

Explanation:

$4 b^{2} + 4 b c + c^{2} - 16$ $color(red)(4b^2+4bc+c^2) - color(blue)(16)$
rewrite the frist 3 terms as a square
$XXXX$ $color(white)("XXXX")$ ${(2 b + c)}^{2} - 4^{2}$ $color(red)((2b+c)^2) - color(blue)(4^2)$
this is the difference of squares with a well-know factoring
$XXXX$ $color(white)("XXXX")$ $(2 b + c + 4) \cdot (2 b + c - 4)$ $(2b+c+4)*(2b+c-4)$

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How do you factor by grouping $4 b^{2} + 4 b c + c^{2} - 16$ $4b^2+4bc+c^2-16$ ?

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How do you factor by grouping 4b2+4bc+c2−164b^2+4bc+c^2-16?

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How do you factor by grouping $4 b^{2} + 4 b c + c^{2} - 16$ $4b^2+4bc+c^2-16$ ?