How do you simplify ${(u + 7 v)}^{2}$ $(u + 7v ) ^ { 2}$ ?

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How do you simplify ${(u + 7 v)}^{2}$ $(u + 7v ) ^ { 2}$ ?

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Answer 1 · 2017-06-26T23:21:10

$u^{2} + 14 u v + 49 v^{2}$ $u^2+14uv+49v^2$

Explanation:

$(u + 7 v) (u + 7 v)$ $(color(blue)(u)color(darkred)(+7v))(color(red)(u)color(green)(+7v))$

You proceed to FOIL it:

Where you multiply the $first term$ $color(blue)"first term"$ with the $outer term$ $color(red)"outer term"$ then you multiply the $first term$ $color(blue)"first term"$ with the $inner term$ $color(green)"inner term"$ :

$(u) (u) = u^{2}$ $(color(blue)(u))(color(red)(u))=u^2$

$(u) (7 v) = 7 u v$ $(color(blue)(u))(color(green)(7v))=7uv$

Now you multiply the $last term$ $color(darkred)"last term"$ with the $outer term$ $color(red)"outer term"$ then you multiply the $last term$ $color(darkred)"last term"$ with the $inner term$ $color(green)"inner term"$ :

$(7 v) (u) = 7 u v$ $color(darkred)((7v))(color(red)(u))=7uv$

$(7 v) (7 v) = 49 v^{2}$ $color(darkred)((7v))(color(green)(7v))=49v^2$

Now combine them:

$u^{2} + 7 u v + 7 u v + 49 v^{2}$ $u^2+7uv+7uv+49v^2$

Simplify:

$u^{2} + 14 u v + 49 v^{2}$ $u^2+14uv+49v^2$

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How do you simplify ${(u + 7 v)}^{2}$ $(u + 7v ) ^ { 2}$ ?

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How do you simplify ${(u + 7 v)}^{2}$ $(u + 7v ) ^ { 2}$ ?