Question

question 5 of 10
multiply the polynomials.
(4x² + 4x + 6)(7x + 5)
a. 28x³ - 40x² + 70x + 30
b. 28x³ + 8x² + 22x + 30
c. 28x³ + 8x² + 22x - 30
d. 28x³ + 48x² + 62x + 30

Explanation:

Step1: Distribute \(4x^2\)

Multiply \(4x^2\) by each term in \((7x + 5)\): \(4x^2 \cdot 7x = 28x^3\), \(4x^2 \cdot 5 = 20x^2\)

Step2: Distribute \(4x\)

Multiply \(4x\) by each term in \((7x + 5)\): \(4x \cdot 7x = 28x^2\), \(4x \cdot 5 = 20x\)

Step3: Distribute \(6\)

Multiply \(6\) by each term in \((7x + 5)\): \(6 \cdot 7x = 42x\), \(6 \cdot 5 = 30\)

Step4: Combine like terms

Combine \(x^2\) terms: \(20x^2 + 28x^2 = 48x^2\)
Combine \(x\) terms: \(20x + 42x = 62x\)
Combine all terms: \(28x^3 + 48x^2 + 62x + 30\)

Answer:

D. \(28x^3 + 48x^2 + 62x + 30\)