Simplify.
-3 27y - 3 128y
A)4 3 2y - 3 3 y
B)7 3 y
C)3 3 y - 4 3 2y
D)3 - 4 3 2

Question

Quizplus · Accepted Answer

To simplify the expression we can factor out 3 and then use the difference of cubes formula:
3(27y - 128y) = 3(-8)(27y/8 - 128y/8) = 3(-8)(3y - 4)(9y^2 + 12y + 16)
So the simplified expression is 3(4 - 3y)(16 + 12y + 9y^2) which is equivalent to 3(3y - 4) - 4(3y^2 + 4y - 4). Therefore the best choice is C. First, we can simplify each term separately using the rule of exponents:
3 27y = 3 * (3^3)^y = 3 * 3^(3y)
3 128y = 3 * (2^7)^y = 3 * 2^(7y)

Subtracting the second term from the first term, we get:
3 * 3^(3y) - 3 * 2^(7y)

We can't combine these terms any further, so the answer is C.

Simplify. -3 27y - 3 128y