Determine whether $x^2+14x+49$ is a perfect square trinomial, if so, how do you factor it.?

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Answer 1 · 2018-06-12T12:10:42

$(x+7)^2$

And tis is $(x+7)*(x+7)$

Answer 2 · 2018-06-12T14:01:51

$x^2 +14x+49 = (x+7)(x+7) = (x+7)^2$

There are a few things to look for in a perfect square trinomial.

the first term must be a perfect square
the third term must be a perfect square ( and a positive term)
the middle term must be made up of twice the product of the square roots of the first term and third term.

In this case: $color(blue)(x^2)+14x" " color(red)( +49)$

$color(blue)(x^2)$ is a perfect square and $color(blue)(sqrt(x^2) =x)$
$color(red)(49)$ is a perfect square and $color(red)(sqrt(49) =7)$

The middle term consists of $2 xxcolor(blue)(x)xxcolor(red)(7) =14x$

$x^2 +14x+49 = (x+7)(x+7) = (x+7)^2$

Determine whether x^2+14x+49x^2+14x+49 is a perfect square trinomial, if so, how do you factor it.?