Factorise:- 45x(x-2)2+60x(x-2)+20x
Step 1: Simplify the polynomial
45x(x-2)2+60x(x-2)+20x=45xx2+4-4x+60x2-120x+20x=45x3+180x-180x2+60x2-120x+20x=45x3-120x2+80x
Step 2: Factorise the polynomial
=5x9x2-24x+16=5x9x2-12x-12x+16=5x3x(3x-4-4(3x-4)=5x(3x-4)(3x-4)=5x(3x-4)2
Hence, the factors of the equation 45x(x-2)2+60x(x-2)+20x are 5x and (3x-4)2.
Factorise: 5√5x2+20x+3√5
Question 26 Factorise the following: (i) 4x2+20x+25 (ii) 9y2–66yz+121z2 (iii) (2x+13)2−(x−12)2