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

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Can $y = x^{2} - 16 x + 64$ $y=x^2-16x+64$ 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.
$(x - 8) (x - 8)$ $color(blue)((x-8) (x -8)$ are the factors

Explanation:

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

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

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

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot 64 = 64$ $N_1*N_2 = a*c =1*64 = 64$

AND

$N_{1} + N_{2} = b = - 16$ $N_1 +N_2 = b = -16$

After trying out a few numbers we get $N_{1} = - 8$ $N_1 = -8$ and $N_{2} = - 8$ $N_2 =-8$
$- 8 \cdot - 8 = 64$ $-8*-8= 64$ , and $(- 8) + (- 8) = - 16$ $(-8)+(-8)= -16$

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

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

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

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

1 Answer

Explanation:

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Can y=x2−16x+64y=x^2-16x+64 be factored? If so what are the factors ?

1 Answer

Explanation:

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