Question

expand the expression to a polynomial in standard form:
$(2x^2 + 3x + 6)(2x^2 + x - 2)$

Explanation:

Step1: Use distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial:

$$
LATEXBLOCK0
$$

Step2: Simplify each term

Calculate each product:

$$
LATEXBLOCK1
$$

Step3: Combine like terms

Combine terms with the same power of \(x\):

• For \(x^{4}\): \(4x^{4}\)
• For \(x^{3}\): \(2x^{3}+6x^{3}=8x^{3}\)
• For \(x^{2}\): \(-4x^{2}+3x^{2}+12x^{2}=11x^{2}\)
• For \(x\): \(-6x + 6x = 0\)
• Constant term: \(-12\)

So the simplified polynomial is \(4x^{4}+8x^{3}+11x^{2}-12\)

Answer:

\(4x^{4}+8x^{3}+11x^{2}-12\)