Question

Which expressions are polynomials? Select each correct answer.

Answer 1

Here's an example

Simplify by collecting like terms: 4(x2y  + 7y) – 5y(3x2 – y) – 10y

 

A) −11x2y + 5y2 + 18y

 

B) 4x2y + 11y – 8yx2 – 16y

 

C) 4x2y + 18y – 15yx2 + 5y2

 

D) 4x2y – 5y(3x2 – y) – 3y

 

A) −11x2y + 5y2 + 18y

Correct. 4(x2y  + 7y) – 5y(3x2 – y) – 10y = 4x2y + 28y – 15yx2 + 5y2 – 10y = 4x2y + 18y – 15yx2 + 5y2 = −11x2y + 5y2 + 18y.

 

B) 4x2y + 11y – 8yx2 – 16y

Incorrect. The 4 is distributed to both terms in the parentheses by multiplying each term by 4 resulting in 28y, not 11y. The −5y is similarly distributed to each term in the parentheses, resulting in −15yx2 + 5y2. The correct answer is −11x2y + 5y2 + 18y.

 

C) 4x2y + 18y – 15yx2 + 5y2

Incorrect. This polynomial can be further simplified by combining the like terms 4x2y and −15yx2. The order of the variables in a term does not matter. The correct answer is

−11x2y + 5y2 + 18y.

 

D) 4x2y – 5y(3x2 – y) – 3y

Incorrect. Before combining like terms, you must distribute to clear the parentheses. The correct answer is −11x2y + 5y2 + 18y.