Question

Which expression is equal to (x−3(−4x²+12x+1) ?

a. −4x²+24x²−35x−3
b. −4x³−35x−3
c. None of the options
d. −4x³+24x²−36x+3
e. −4x³+12x²−36x−3

Answer 1

The expanded form of the expression (x-3)(-4x²+12x+1) is -4x³ + 24x² - 36x - 3, which matches option d.

Step-by-step explanation:

To solve the expression (x-3)(-4x²+12x+1), we need to distribute x and -3 across the terms inside the parentheses. The expression can be expanded by multiplying each term in the first set of parentheses successively by each term in the second set of parentheses. This will give us four individual products:

• x times -4x² which equals -4x³,
• x times 12x which equals 12x²,
• x times 1 which equals x,
• -3 times -4x² which equals 12x²,
• -3 times 12x which equals -36x,
• -3 times 1 which equals -3.

Combining the like terms 12x² and 12x², we get 24x². The expression simplified is -4x³ + 24x² - 36x - 3, which corresponds to option d.