expand the expression to a polynomial in standard form: (4x - 3)(x - 1)(2x - 3)

Question

Accepted Answer

# Explanation:
## Step1: Multiply the first two binomials
First, we multiply $(4x - 3)$ and $(x - 1)$ using the distributive property (FOIL method).
$$
\begin{align*}
(4x - 3)(x - 1)&=4x\times x+4x\times(-1)-3\times x - 3\times(-1)\
&=4x^{2}-4x - 3x + 3\
&=4x^{2}-7x + 3
\end{align*}
$$
## Step2: Multiply the result by the third binomial
Now we multiply the quadratic $4x^{2}-7x + 3$ with the binomial $(2x - 3)$.
$$
\begin{align*}
&(4x^{2}-7x + 3)(2x - 3)\
=&4x^{2}\times(2x)+4x^{2}\times(-3)-7x\times(2x)-7x\times(-3)+3\times(2x)+3\times(-3)\
=&8x^{3}-12x^{2}-14x^{2}+21x + 6x-9\
=&8x^{3}+(-12x^{2}-14x^{2})+(21x + 6x)-9\
=&8x^{3}-26x^{2}+27x - 9
\end{align*}
$$

# Answer:
$8x^{3}-26x^{2}+27x - 9$

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QUESTION IMAGE

Question

Explanation:

Step1: Multiply the first two binomials

Step2: Multiply the result by the third binomial

Answer: