Question

Consider the expression 3x^2 + 5y^2 + 3. Identify the terms to be placed in the boxes to make the expression equivalent to 9x^2 - y^2 + 9.

a. Positive 6x^2 and Negative 6y^2
b. Positive 6x^2 and Negative 10y^2
c. Positive 9x^2 and Negative 10y^2
d. Positive 9x^2 and Negative 6y^2

Answer 1

To transform 3x^2 + 5y^2 + 3 into 9x^2 - y^2 + 9, add Positive 6x^2 and subtract Negative 6y^2 from the original expression.

Option a is correct.

Step-by-step explanation:

To make the expression 3x2 + 5y2 + 3 equivalent to 9x2 - y2 + 9, we must find the terms to add or subtract from the original expression.

We need our x2 term to go from 3x2 to 9x2, which means we should add 6x2 (since 3x2 + 6x2 = 9x2). Similarly, we need our y2 term to go from 5y2 to -y2, requiring us to subtract 6y2 (because 5y2 - 6y2 = -y2).

The constant term is already the same (+3) in both expressions, so no change is required there. Therefore, the correct terms to make the two expressions equivalent are Positive 6x2 and Negative 6y2.

Option a is correct.