How do you write d^2-18d+80d2−18d+80 in factored form?

1 Answer
Don't Memorise
Sep 16, 2015

color(blue)((d-8)(d-10) (d−8)(d−10) is the factorised form of the expression.

Explanation:

d^2 -18d +80d2−18d+80

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

In this technique, if we have to factorise an expression like ad^2 + bd + cad2+bd+c, we need to think of 2 numbers such that:

N_1*N_2 = a*c = 1*80 = 80N1⋅N2=a⋅c=1⋅80=80
and
N_1 +N_2 = b = -18N1+N2=b=−18

After trying out a few numbers we get N_1 = -10N1=−10 and N_2 =-8N2=−8
-10*-8 = 80−10⋅−8=80, and (-10)+(-8)= -18(−10)+(−8)=−18

d^2 -18d +80= d^2 -10d-8d +80d2−18d+80=d2−10d−8d+80

=d(d-10) -8(d -10)=d(d−10)−8(d−10)

=color(blue)((d-8)(d-10) =(d−8)(d−10)

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