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

Given equation:
45x(x-2)²+60x(x-2)+20x

On solving the brackets of the above equation we get

45x( x2- 4x +4) + 60×2- 120x + 20x

= 45x3– 180×2+ 180x + 60x2 – 100x

= 45×3 – 120×2 + 80x

Taking out 5x as a common factor we get,

=5x (9×2 – 24x + 16)

Now will factoriese the bracketted equation

=5x{(3x)2 -12x-12x +16}

= 5x { 3x(3x-4) -4(3x-4)}

= 5x{(3x-4)2}

Hence, On factorising 45x(x-2)²+60x(x-2)+20x we get 5x{(3x-4)2)

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