Question

question 4 of 6
select the correct answer.
what is the standard form of this expression?
(3x + 4)(x - 8)
3x² - 4x - 32
3x² - 20x - 32
3x² - 20x - 12
3x² - 4x - 12

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first binomial by each term in the second binomial:
$$(3x + 4)(x - 8)=3x\cdot x+3x\cdot(-8)+4\cdot x + 4\cdot(-8)$$

Step2: Simplify each term

Simplify the products:
$$3x\cdot x = 3x^{2}, \quad 3x\cdot(-8)=-24x, \quad 4\cdot x = 4x, \quad 4\cdot(-8)=-32$$
So the expression becomes:
$$3x^{2}-24x + 4x-32$$

Step3: Combine like terms

Combine the $x$ - terms:
$$-24x + 4x=-20x$$
So the simplified expression is:
$$3x^{2}-20x - 32$$

Answer:

B. \(3x^{2}-20x - 32\)