How do you factor the expression $x^2 + 4x + 4$ ?

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Answer 1 · 2016-03-16T12:36:10

$color(green)( (x+2) (x+2)$ is the factorised form of the expression.

$x^2 + 4x +4$

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:

$N_1*N_2 = a*c = 1*4= 4$

AND

$N_1 +N_2 = b = 4$

After trying out a few numbers we get $N_1 = 2$ and $N_2 =2$

$2*2 = 4$ , and $2+ 2 = 4$

$x^2 + color(green)(4x) +4 = x^2 + color(green)(2x + 2x) +4$

$= x (x+2) + 2 ( x +2 )$

$= (x+2) (x+2)$

$color(green)( (x+2) (x+2)$ is the factorised form of the expression.

How do you factor the expression x^2 + 4x + 4x^2 + 4x + 4?