Question
Simplify: $(5 - x)(6 - 5x)( 2 - x)$
✓
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 $60-92 x+41 x^2-5 x^3$.
$ (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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