Question

what is the product?\
(2x - 1)(x + 4)\
\bigcirc\\ 2x^2 - 4\
\bigcirc\\ 2x^2 + 4\
\bigcirc\\ 2x^2 + 7x - 4\
\bigcirc\\ 2x^2 - 7x - 4

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
$(2x - 1)(x + 4) = 2x \cdot x + 2x \cdot 4 - 1 \cdot x - 1 \cdot 4$

Step2: Simplify each term

Calculate each product:
$2x \cdot x = 2x^2$, $2x \cdot 4 = 8x$, $-1 \cdot x = -x$, $-1 \cdot 4 = -4$

Step3: Combine like terms

Combine the $x$-terms:
$2x^2 + 8x - x - 4 = 2x^2 + 7x - 4$

Answer:

$2x^2 + 7x - 4$ (corresponding to the option "2x² + 7x - 4")