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

Jan 12, 2016

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

#### Explanation:

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

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

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 64 = 64$

AND

${N}_{1} + {N}_{2} = b = - 16$

After trying out a few numbers we get ${N}_{1} = - 8$ and ${N}_{2} = - 8$
$- 8 \cdot - 8 = 64$, and $\left(- 8\right) + \left(- 8\right) = - 16$

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

$= x \left(x - 8\right) - 8 \left(x - 8\right)$

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