Question

Which expressions are equivalent to 6xy +9xy - 18y? select all that apply

A.3(2xy + 3xy - 6y)
B. 3x(2y + 3y - 6)
C. 3y(2x + 3x -6)
D. xy(5 - 6y)
E. 3y(5x - 6)
F. y(15x - 18)

Answer 1

FIRST
We could use distribution property because the coefficient of each term has the same factor. The coefficients are 6, 9, -18. They have same factor 3 and y.

Now we distribute the factor
6xy + 9xy - 18y
= 3 × 2 xy + 3 × 3 xy - 3 × 6 y
= 3(2xy + 3xy - 6y)
= 3y (2x + 3x - 6)

SECOND
Before we distribute the algebra form, we simplify it first by adding the terms that have same variables. In this case, first term (6xy) and second term (9xy) should be added.
6xy + 9xy - 18y
= 15xy - 18y

The terms above has 2 same factor, 3 and y. Distribute it.
15xy - 18y
= 3 × 5 xy - 3 × 6 y
= 3(5xy - 6y)
= y(15x - 18)
= 3y(5x - 6)

So the answers are option A, C, E, F

Answer 2

So here just simplify all of the answer choices.
A gets you 6xy + 9xy - 18y, so that's correct.
B gets you 6xy + 9xy - 18x, which is wrong.
C is 6xy + 9xy - 18y, which is correct.
D is 5xy - 6xy^2, which is wrong.
E gets you 15xy - 18y, which is correct because it is the simplified version of the original equation.
F gets you 15xy - 18y, which is also correct.

So choose A, C, E, and F.