Question

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

Explanation:

Step1: Multiply the first two binomials

First, multiply \((3x - 4)\) and \((2x + 1)\). Using the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

Step2: Multiply the last two binomials

Next, multiply \((x + 2)\) and \((x + 1)\):

$$
LATEXBLOCK1
$$

Step3: Multiply the two resulting trinomials

Now, multiply \((6x^2 - 5x - 4)\) and \((x^2 + 3x + 2)\):

$$
LATEXBLOCK2
$$

Step4: Combine like terms

Combine the like terms:

• For \(x^4\): \(6x^4\)
• For \(x^3\): \(18x^3 - 5x^3 = 13x^3\)
• For \(x^2\): \(12x^2 - 15x^2 - 4x^2 = -7x^2\)
• For \(x\): \(-10x - 12x = -22x\)
• Constant term: \(-8\)

Putting it all together, we get:

$$ 6x^4 + 13x^3 - 7x^2 - 22x - 8 $$

Answer:

\(6x^4 + 13x^3 - 7x^2 - 22x - 8\)