How do you factor the trinomial $x^2 + 14x + 49$ ?

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Answer 1 · 2015-11-19T22:19:43

$(x+7)^2$

Suppose we have the variables 'a' and 'b' where

$ab=49$
$a+b=14$

Note that this approach only works if the coefficient of $x^2$ is 1.
That is: $x^2 -= 1 times x^2color(white)(xxxxxx) ( or 1x)$

$7 times 7 =49$
$7+7 =14$

So we have:

$(x+7)(x+7) -= (x+7)^2$

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Foot note for reference:
$(x+7)(x+7) " is the same as " x(x+7) + 7(x+7)$

How do you factor the trinomial x^2 + 14x + 49 x^2 + 14x + 49 ?