Question

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

Explanation:

Step1: Multiply the first two binomials

First, multiply \((x + 1)\) and \((x - 3)\) using the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

Step2: Multiply the last two binomials

Next, multiply \((2x - 3)\) and \((3x - 2)\) using the distributive property:

$$
LATEXBLOCK1
$$

Step3: Multiply the two resulting trinomials

Now, multiply \((x^{2}-2x - 3)\) and \((6x^{2}-13x + 6)\):

$$
LATEXBLOCK2
$$

Step4: Combine like terms

Combine the like terms:

• For \(x^{4}\): \(6x^{4}\)
• For \(x^{3}\): \(-13x^{3}-12x^{3}=-25x^{3}\)
• For \(x^{2}\): \(6x^{2}+26x^{2}-18x^{2}=14x^{2}\)
• For \(x\): \(-12x + 39x = 27x\)
• Constant term: \(-18\)

So the polynomial in standard form is \(6x^{4}-25x^{3}+14x^{2}+27x - 18\)

Answer:

\(6x^{4}-25x^{3}+14x^{2}+27x - 18\)