Question
Simplify:
$(5 x+3)(x-1)(3 x-2)$
$(5 x+3)(x-1)(3 x-2)$
✓
Answer
To simplify, we will proceed as follows:
$(5 x+3)(x-1)(3 x-2)$
$=[(5 x+3)(x-1)](3 x-2)$
$=[5 x(x-1)+3(x-1)](3 x-2)$
$=\left[5 x^2-5 x+3 x-3\right](3 x-2)(\text { Distributive law) }$
$=\left[5 x^2-2 x-3\right](3 x-2)$
$=3 x\left(5 x^2-2 x-3\right)-2\left(5 x^2-2 x-3\right)$
$=15 x^3-6 x^2-9 x-\left[10 x^2-4 x-6\right]$
$=15 x^3-6 x^2-9 x-10 x^2+4 x+6$
$=15 x^3-6 x^2-10 x^2-9 x+4 x+6 \text { (Rearranging) }$
$=15 x^3-16 x^2-5 x+6 \text { (Combining like terms) }$
Thus, the answer is $15 x^3-16 x^2-5 x+6$.
$(5 x+3)(x-1)(3 x-2)$
$=[(5 x+3)(x-1)](3 x-2)$
$=[5 x(x-1)+3(x-1)](3 x-2)$
$=\left[5 x^2-5 x+3 x-3\right](3 x-2)(\text { Distributive law) }$
$=\left[5 x^2-2 x-3\right](3 x-2)$
$=3 x\left(5 x^2-2 x-3\right)-2\left(5 x^2-2 x-3\right)$
$=15 x^3-6 x^2-9 x-\left[10 x^2-4 x-6\right]$
$=15 x^3-6 x^2-9 x-10 x^2+4 x+6$
$=15 x^3-6 x^2-10 x^2-9 x+4 x+6 \text { (Rearranging) }$
$=15 x^3-16 x^2-5 x+6 \text { (Combining like terms) }$
Thus, the answer is $15 x^3-16 x^2-5 x+6$.
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