Simplify: (5x + 3)(x − 1)(3x − 2)


(5x + 3)(x − 1)(3x − 2)


To simplify, we will proceed as follows:

(5x + 3)(x − 1)(3x − 2)

$=[(5 x+3)(x-1)](3 x-2)$

$=[5 x(x-1)+3(x-1)](3 x-2)$      (Distributive law)

$=\left[5 x^{2}-5 x+3 x-3\right](3 x-2)$

$=\left[5 x^{2}-2 x-3\right](3 x-2)$

$=3 x\left(5 x^{2}-2 x-3\right)-2\left(5 x^{2}-2 x-3\right)$

$=15 x^{3}-6 x^{2}-9 x-\left[10 x^{2}-4 x-6\right]$

$=15 x^{3}-6 x^{2}-9 x-10 x^{2}+4 x+6$

$=15 x^{3}-6 x^{2}-10 x^{2}-9 x+4 x+6 \quad$ (Rearranging)

$=15 x^{3}-16 x^{2}-5 x+6 \quad$ (Combining like terms)

Thus, the answer is $15 x^{3}-16 x^{2}-5 x+6$.



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