Which expression is equivalent to 3x(x + 2)(x - 3)
A 3x ^ 2 - 3x ^ 2 - 18x
B 3x ^ 2 - 3x ^ 2 + 3x - 6
C 3x ^ 2 - 3x ^ 2 + 18x
D 3x ^ 2 + 3x ^ 2 + 7x - 3
The correct expression that is equivalent to 3x(x + 2)(x - 3) is:
C) 3x^2 - 3x^2 + 18x
To simplify the expression 3x(x + 2)(x - 3), we need to apply the distributive property.
Step 1: Distribute 3x to (x + 2)
3x * x = 3x^2
3x * 2 = 6x
So, the expression becomes: 3x^2 + 6x(x - 3)
Step 2: Distribute 6x to (x - 3)
6x * x = 6x^2
6x * -3 = -18x
The fully simplified expression is thus: 3x^2 + 6x(x - 3) = 3x^2 + 6x^2 - 18x.
Therefore, the answer is A) 3x^2 - 3x^2 - 18x.