Simplify: (x^2-3 x+2 )(5 x-2)- (3 x^2+4 x-5 )(2 x-1) - Vidyadip

Question

Simplify:
$\left(x^2-3 x+2\right)(5 x-2)-\left(3 x^2+4 x-5\right)(2 x-1)$

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Answer

To simplify, we will proceed as follows: $\left(x^2-3 x+2\right)(5 x-2)-\left(3 x^2+4 x-5\right)(2 x-1)$
$=\left[\left(x^2-3 x+2\right)(5 x-2)\right]-\left[\left(3 x^2+4 x-5\right)(2 x-1)\right]$
$=\left[5 x\left(x^2-3 x+2\right)-2\left(x^2-3 x+2\right)\right]-\left[2 x\left(3 x^2+4 x-5\right)-1 \times\left(3 x^2+4 x-5\right)\right] \text { (Distributive law) }$
$=\left[5 x^3-15 x^2+10 x-\left(2 x^2-6 x+4\right)\right]-\left[6 x^3+8 x^2-10 x-3 x^2-4 x+5\right]$
$=5 x^3-15 x^2+10 x-2 x^2+6 x-4-6 x^3-8 x^2+10 x+3 x^2+4 x-5$
$=5 x^3-6 x^3-15 x^2-2 x^2-8 x^2+3 x^2+10 x+6 x+10 x+4 x-5-4 \text { (Rearranging) }$
$=-x 3-22 x^2+30 x-9 \text { (Combining like terms) }$
Thus, the answer is $-x 3-22 x^2+30 x-9$.

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