Question

44 multiply/distribute the expression. use generic rectangles or any method. use paper to record your work.

(3x - 2)(4x² - 5x + 1)

Explanation:

Step1: Distribute \(3x\)

Multiply \(3x\) by each term in \(4x^2 - 5x + 1\):
\(3x \cdot 4x^2 = 12x^3\), \(3x \cdot (-5x) = -15x^2\), \(3x \cdot 1 = 3x\).

Step2: Distribute \(-2\)

Multiply \(-2\) by each term in \(4x^2 - 5x + 1\):
\(-2 \cdot 4x^2 = -8x^2\), \(-2 \cdot (-5x) = 10x\), \(-2 \cdot 1 = -2\).

Step3: Combine like terms

Add the results from Step1 and Step2:
\(12x^3 - 15x^2 + 3x - 8x^2 + 10x - 2\).
Combine \(x^2\) terms: \(-15x^2 - 8x^2 = -23x^2\).
Combine \(x\) terms: \(3x + 10x = 13x\).

Answer:

\(12x^3 - 23x^2 + 13x - 2\)