Question

which expression is equivalent to (2x - 1)(4x + 3) - (9x + 1)(2x - 1)?
a. -10x² - x - 2
b. -10x² + 9x - 2
c. -10x² - 5x - 4
d. -10x² + 21x - 4

Explanation:

Step1: Factor out \((2x - 1)\)

Notice that both terms have a common factor of \((2x - 1)\). So we can factor it out:
\[
(2x - 1)[(4x + 3) - (9x + 1)]
\]

Step2: Simplify the expression inside the brackets

Simplify \((4x + 3) - (9x + 1)\):
\[
4x + 3 - 9x - 1 = -5x + 2
\]
Now our expression becomes \((2x - 1)(-5x + 2)\)

Step3: Expand the product

Use the distributive property (FOIL method) to expand \((2x - 1)(-5x + 2)\):
\[
2x(-5x) + 2x(2) - 1(-5x) - 1(2)
\]
\[
= -10x^2 + 4x + 5x - 2
\]

Step4: Combine like terms

Combine the \(x\)-terms:
\[
-10x^2 + (4x + 5x) - 2 = -10x^2 + 9x - 2
\]

Answer:

B. \(-10x^2 + 9x - 2\)