Simplify: (5-x)(6-5 x)(2-x) - Vidyadip

Question

Simplify:
$(5-x)(6-5 x)(2-x)$

✓

Answer

To simplify, we will proceed as follows:( 5 - x $)(6-5 x)(2-x)$
$=[(5-x)(6-5 x)](2-x)$
$=[5(6-5 x)-x(6-5 x)](2-x)(\text { Distributive law) }$
$=\left(30-25 x-6 x+5 x^2\right)(2-x)$
$=\left(30-31 x+5 x^2(2-x)\right.$
$=2\left(30-31 x+5 x^2\right)-x\left(30-31 x+5 x^2\right)$
$=60-62 x+10 x^2-30 x+31 x^2-5 x^3$
$=60-62 x+10 x^2-30 x+31 x^2-5 x^3$
$=60-62 x-30 x+10 x^2+31 x^2-5 x^3 \text { (Rearranging) }$
$=60-92 x+41 x^2-5 x^3 \text { Combining like terms) }$
Thus, the answer is $60-92 x+41 x^2-5 x^3$.

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