Question

Simplify:
(5 − x)(6 − 5x)( 2 − x)

Answer 1

To simplify, we will proceed as follows:

$$\begin{gathered} \left(5-x\right)\left(6-5x\right)\left(2-x\right) \\ =\left[\left(5-x\right)\left(6-5x\right)\right]\left(2-x\right) \end{gathered}$$
$=\left[5\left(6-5x\right)-x\left(6-5x\right)\right]\left(2-x\right)$ (Distributive law)
$$\begin{gathered} =\left(30-25x-6x+5x^2\right)\left(2-x\right) \\ =\left(30-31x+5x^2\right)\left(2-x\right) \\ =2\left(30-31x+5x^2\right)-x\left(30-31x+5x^2\right) \\ =60-62x+10x^2-30x+31x^2-5x^3 \end{gathered}$$
$=60-62x-30x+10x^2+31x^2-5x^3$ (Rearranging)
$=60-92x+41x^2-5x^3$ (Combining like terms)

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