How do you write $x^2 + 8x + 16$ in factored form?

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Answer 1 · 2015-09-16T16:10:00

$color(blue)((x+4)(x+4)$

$x^2+8x+16$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 4*4 =16$
and
$N_1 +N_2 = b = 8$

After trying out a few numbers we get $N_1 = 4$ and $N_2 =4$
$4*4 = 16$ and $4+4=8$

$x^2+8x+16=x^2+4x +4x+16$
$=x(x+4)+4(x+4)$

$color(blue)((x+4)(x+4)$

How do you write x^2 + 8x + 16 x^2 + 8x + 16 in factored form?