How do you factor $8n^2 - 8n +2$ ?

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Answer 1 · 2015-09-22T16:49:08

$=color(blue)((4n-2) ( 2n-1)$ is the factorised form of the expression.

$8n^2 -8n +2$

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

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

$N_1*N_2 = a*c = 8*2 = 16$

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 $(-4) +(-4)= -8$

$8n^2 -color(blue)(8n) +2 = 8n^2 color(blue)(-4n - 4n) +2$

$=4n( 2n-1) - 2 (2n -1)$

$color(blue)((4n-2) ( 2n-1)$ is the factorised form of the expression.

How do you factor 8n^2 - 8n +28n^2 - 8n +2?