Question

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

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:

\(8x^{3}-26x^{2}+27x - 9\)