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Which expressions are equivalent to [tex]6xy + 9xy - 18y[/tex]? Circle all that apply.

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



Answer :

GinnyAnswer
To determine which expressions are equivalent to [tex]\(6xy + 9xy - 18y\)[/tex], we need to simplify and compare them.

Let's start simplification of the original expression:
[tex]\[ 6xy + 9xy - 18y \][/tex]
Combine like terms:
[tex]\[ (6xy + 9xy) - 18y = 15xy - 18y \][/tex]

Now, we will compare [tex]\(15xy - 18y\)[/tex] with each of the provided options:

A. [tex]\(3(2xy + 3xy - 6y)\)[/tex]

First, simplify within the parentheses:
[tex]\[ 2xy + 3xy - 6y = 5xy - 6y \][/tex]

Then, distribute the 3:
[tex]\[ 3(5xy - 6y) = 15xy - 18y \][/tex]
This matches [tex]\(15xy - 18y\)[/tex].

B. [tex]\(3x(2y + 3y - 6)\)[/tex]

First, simplify within the parentheses:
[tex]\[ 2y + 3y - 6 = 5y - 6 \][/tex]

Then, distribute the 3x:
[tex]\[ 3x(5y - 6) = 15xy - 18x \][/tex]
This expression does not match [tex]\(15xy - 18y\)[/tex].

C. [tex]\(3y(2x + 3 x - 6)\)[/tex]

First, simplify within the parentheses:
[tex]\[ 2x + 3x - 6 = 5x - 6 \][/tex]

Then, distribute the 3y:
[tex]\[ 3y(5x - 6) = 15xy - 18y \][/tex]
This matches [tex]\(15xy - 18y\)[/tex].

D. [tex]\(xy(5 - 6y)\)[/tex]

Distribute the [tex]\(xy\)[/tex]:
[tex]\[ xy(5 - 6y) = 5xy - 6xy^2 \][/tex]
This form does not match [tex]\(15xy - 18y\)[/tex].

E. [tex]\(3y(5x - 6)\)[/tex]

Distribute the 3y:
[tex]\[ 3y(5x - 6) = 15xy - 18y \][/tex]
This matches [tex]\(15xy - 18y\)[/tex].

F. [tex]\(y(15x - 18)\)[/tex]

Distribute the [tex]\(y\)[/tex]:
[tex]\[ y(15x - 18) = 15xy - 18y \][/tex]
This matches [tex]\(15xy - 18y\)[/tex].

Hence, the expressions equivalent to [tex]\(6xy + 9xy - 18y\)[/tex] are:
[tex]\[ \boxed{\text{A, C, E, and F}} \][/tex]

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