Can $y=x^2-16x+64$ be factored? If so what are the factors ?

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Answer 1 · 2016-01-12T17:47:06

Yes the expression can be factorised.
$color(blue)((x-8) (x -8)$ are the factors

$y = x^2 -16x +64$

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:

$N_1*N_2 = a*c =1*64 = 64$

AND

$N_1 +N_2 = b = -16$

After trying out a few numbers we get $N_1 = -8$ and $N_2 =-8$
$-8*-8= 64$ , and $(-8)+(-8)= -16$

$=x^2 -16x +64 = x^2 -8x -8x+64$

$= x(x -8) -8(x-8)$

$=color(blue)((x-8) (x -8)$

Can y=x^2-16x+64 y=x^2-16x+64 be factored? If so what are the factors ?