Question

(3x - 2)(5x² + 2x - 1) = ___\
a. 8x³ - 4x² - 7x + 2\
b. 15x³ - 4x² - 7x + 2\
c. 15x³ - 3x² - 5x + 2\
d. 15x³ - 8x² - 4x - 2\
type in the letter of the correct choice: a, b, c or d\
\
question 7\
1 pts\
5x²(4x + 1) = ___\
a. 9x³ + 5x²\
b. 20x² + 5x\
c. 20x³ + 5x²\
d. 20x³ + 1\
type in the letter of the correct choice: a, b, c or d

Explanation:

First Question ( \((3x - 2)(5x^2 + 2x - 1)\) )

Step1: Distribute \(3x\)

Multiply \(3x\) with each term in \(5x^2 + 2x - 1\):
\(3x \cdot 5x^2 = 15x^3\), \(3x \cdot 2x = 6x^2\), \(3x \cdot (-1) = -3x\).

Step2: Distribute \(-2\)

Multiply \(-2\) with each term in \(5x^2 + 2x - 1\):
\(-2 \cdot 5x^2 = -10x^2\), \(-2 \cdot 2x = -4x\), \(-2 \cdot (-1) = 2\).

Step3: Combine like terms

Combine the results:
\(15x^3 + 6x^2 - 3x - 10x^2 - 4x + 2\)
Combine \(x^2\) terms: \(6x^2 - 10x^2 = -4x^2\)
Combine \(x\) terms: \(-3x - 4x = -7x\)
Final expression: \(15x^3 - 4x^2 - 7x + 2\).

Second Question ( \(5x^2(4x + 1)\) )

Step1: Distribute \(5x^2\)

Multiply \(5x^2\) with each term in \(4x + 1\):
\(5x^2 \cdot 4x = 20x^3\), \(5x^2 \cdot 1 = 5x^2\).

Answer:

First question: B
Second question: C