Simplify: (5 x+3)(x-1)(3 x-2) - Vidyadip

Question

Simplify: $ (5 x+3)(x-1)(3 x-2) $

✓

Answer

To simplify, we will proceed as follows:
$ (5 x+3)(x-1)(3 x-2) $
$ =[(5 x+3)(x-1)](3 x-2) $
$ =[5 x(x-1)+3(x-1)](3 x-2) $
$ =\left[5 x^2-5 x+3 x-3\right](3 x-2) \text { (Distributive law) } $
$ =\left[5 x^2-2 x-3\right](3 x-2) $
$ =3 x\left(5 x^2-2 x-3\right)-2\left(5 x^2-2 x-3\right) $
$ =15 x^3-6 x^2-9 x-\left[10 x^2-4 x-6\right] $
$ =15 x^3-6 x^2-9 x-10 x^2+4 x+6 $
$ =15 x^3-6 x^2-10 x^2-9 x+4 x+6 \text { (Rearranging) } $
$ =15 x^3-16 x^2-5 x+6 \text { (Combining like terms) }$
Thus, the answer is $15 x^3-16 x^2-5 x+6$

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