Question

what is the result of multiplying the binomials (2x - 3) and (x + 2)? 2x^2 - 7x - 6; 2x^2 + x - 6; 2x^2 - x - 6; 2x^2 + 7x - 6

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
$(2x - 3)(x + 2) = 2x \cdot x + 2x \cdot 2 - 3 \cdot x - 3 \cdot 2$

Step2: Simplify each product

Calculate each term:
$2x \cdot x = 2x^2$, $2x \cdot 2 = 4x$, $-3 \cdot x = -3x$, $-3 \cdot 2 = -6$

Step3: Combine like terms

Combine the middle terms ($4x - 3x$):
$2x^2 + (4x - 3x) - 6 = 2x^2 + x - 6$

Answer:

B. $2x^2 + x - 6$ (assuming the purple option is labeled B; if labels differ, the expression is $2x^2 + x - 6$)