How do you factor 9z^2-12z+49z2−12z+4?

1 Answer
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May 28, 2015

9z^2-12z+49z2−12z+4

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like az^2 + bz + caz2+bz+c, we need to think of 2 numbers such that:
N_1*N_2 = a*c = 9*4 = 36N1⋅N2=a⋅c=9⋅4=36
and
N_1 +N_2 = b = -12N1+N2=b=−12
After trying out a few numbers we get N_1 = -6N1=−6 and N_2 =-6N2=−6
-6*(-6) = 36−6⋅(−6)=36, and (-6)+(-6)= -12(−6)+(−6)=−12

9z^2-12z+4 = 9z^2-6z - 6z+49z2−12z+4=9z2−6z−6z+4

=3z(3z - 2) -2(3z-2)=3z(3z−2)−2(3z−2)
=color(green)((3z-2)(3z-2)=(3z−2)(3z−2)

note : We know that color(green)((a - b)^2 = a^2- 2ab + b^2)(a−b)2=a2−2ab+b2

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