Question

multiply. (simplify your answer completely.)
(6x² + x - 3)(8x² + x - 1)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial:
$$(6x^2 + x - 3)(8x^2 + x - 1)$$
$$= 6x^2 \cdot 8x^2 + 6x^2 \cdot x + 6x^2 \cdot (-1) + x \cdot 8x^2 + x \cdot x + x \cdot (-1) - 3 \cdot 8x^2 - 3 \cdot x - 3 \cdot (-1)$$

Step2: Simplify each product

Calculate each term:
$$= 48x^4 + 6x^3 - 6x^2 + 8x^3 + x^2 - x - 24x^2 - 3x + 3$$

Step3: Combine like terms

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

• For \(x^4\): \(48x^4\)
• For \(x^3\): \(6x^3 + 8x^3 = 14x^3\)
• For \(x^2\): \(-6x^2 + x^2 - 24x^2 = -29x^2\)
• For \(x\): \(-x - 3x = -4x\)
• Constant term: \(3\)

So the simplified form is:
$$48x^4 + 14x^3 - 29x^2 - 4x + 3$$

Answer:

\(48x^4 + 14x^3 - 29x^2 - 4x + 3\)