How do you factor the expression $x^2 - 8x + 16$ ?

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Answer 1 · 2016-01-18T17:18:03

$color(blue)(( x-4) (x-4)$ is the factorised form of the expression.

$x^2-8x+16$

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:

$N_1*N_2 = a*c = 1*16 =16$

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

$x^2-color(blue)(8x)+16 = x^2-color(blue)(4x-4x)+16$

$= x(x-4) -4(x-4)$

$= color(blue)(( x-4) (x-4)$

How do you factor the expression x^2 - 8x + 16x^2 - 8x + 16?