Question

find the product.

\\((4x^2 + 2)(6x^2 + 8x + 5)\\)

type the correct answer in each box. use numerals instead of words.

\\(\quadx^4 + \quadx^3 + \quadx^2 + \quadx + \quad\\)

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Distribute the terms

$$ (4x^2 + 2)(6x^2 + 8x + 5) = 4x^2(6x^2 + 8x + 5) + 2(6x^2 + 8x + 5) $$

Step 2: Multiply each part

$$ 4x^2(6x^2 + 8x + 5) = 24x^4 + 32x^3 + 20x^2 $$

$$ 2(6x^2 + 8x + 5) = 12x^2 + 16x + 10 $$

Step 3: Combine like terms

$$ 24x^4 + 32x^3 + (20x^2 + 12x^2) + 16x + 10 $$

$$ 24x^4 + 32x^3 + 32x^2 + 16x + 10 $$

Answer:

24\(x^4\) + 32\(x^3\) + 32\(x^2\) + 16\(x\) + 10