How do you factor $r^2-4r+4$ ?

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Answer 1 · 2016-05-10T06:12:02

$color(blue)( (r - 2 ) ( r - 2)$ is the factorised form of the expression.

$r^2 - 4r + 4$

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

In this technique, if we have to factorise an expression like $ar^2 + br + c$ , 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 $(-2 ) +( - 2)= - 4$

$r^2 color(blue)(- 4r) + 4 = r^2 color(blue)(- 2r - 2r) + 4$

$= r ( r - 2)- 2 ( r - 2 )$

$= (r - 2 ) ( r - 2)$

How do you factor r^2-4r+4r^2-4r+4?