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Question

Factorise:- 45x(x-2)2+60x(x-2)+20x


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Solution

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.


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