Question

Elaina simplified the algebraic expression below. Hannah claimed that Elaina did not finish the process. Which answer shows the simplified expression that Hannah expected?

[3y^2 + 9y - y^2 + 9 - 2y - 3 = (3y^2 - y^2) + (9y - 2y) + (9 - 3)]

A) (2y^2 - 7y + 6)

B) (2y^2 + 7y + 6)

C) (4y^2 - 7y + 6)

D) (4y^2 + 7y + 6)

Please select the answer that represents the simplified expression as expected by Hannah.

Answer 1

To simplify the expression 3y² + 9y - y² + 9 - 2y - 3, like terms are combined to result in the simplified form 2y² + 7y + 6, which is option B.

Step-by-step explanation:

The expression given needs to be simplified by combining like terms, which are terms that contain the same variable raised to the same power. The process involves adding or subtracting the coefficients (numerical parts) of the like terms. In the expression 3y² + 9y - y² + 9 - 2y - 3, we combine like terms as follows:

• Combine the y² terms: 3y² - y² = 2y²
• Combine the y terms: 9y - 2y = 7y
• Combine the constant terms: 9 - 3 = 6

Putting it all together, the simplified expression is 2y² + 7y + 6, which corresponds to option B).