Simplify: (5 − x)(6 − 5x)( 2 − x)


(5 − x)(6 − 5x)( 2 − x)


To simplify, we will proceed as follows:

(5 − x)(6 − 5x)( 2 − x)

$=[(5-x)(6-5 x)](2-x)$

$=[5(6-5 x)-x(6-5 x)](2-x)$        (Distributive law)             

$=\left(30-25 x-6 x+5 x^{2}\right)(2-x)$

$=\left(30-31 x+5 x^{2}\right)(2-x)$

$=2\left(30-31 x+5 x^{2}\right)-x\left(30-31 x+5 x^{2}\right)$

$=60-62 x+10 x^{2}-30 x+31 x^{2}-5 x^{3}$

$=60-62 x-30 x+10 x^{2}+31 x^{2}-5 x^{3} \quad$ (Rearranging)

$=60-92 x+41 x^{2}-5 x^{3} \quad$ (Combining like terms)

Thus, the answer is $60-92 x+41 x^{2}-5 x^{3}$.


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