Question

Consider the following expression and the simplified expression. Expression Simplified Expression 3x^2+5y +3 +4y^2+6 9x^2-7^2+9 Which terms could be in the boxes to make the expressions equivalent?

Answer 1

The correct answer option is
`+6x^2` and
`-10y^2`.

Explanation:

We are given the following incomplete expression:

`3 x^2 + 5 y^2` __
`+ 3` __
`+ 4 y^2 + 6`

and then there is its simplified expression as shown below:

`9 x^2 - y^2 + 9`

We are to determine whether which terms could be in the boxes to make the expressions equivalent.

`+6x^2` and
`-10y^2` are the two terms which justify the given expression:

`3 x^2 + 5 y^2 +6x^2 + 3 -10y^2 + 4 y^2 + 6 = 9 x^2 - y^2 + 9`

Answer 2

`+6x^2` and
`-10y^2`

Explanation:

Let's go one term at a time from the right side and match it with the left side.

• On the right hand side, we have
  `9x^2`. On the left side we have
  `3x^2`. So we would need a
  `6x^2`. Hence we can eliminate option C and D immediately.

• On the right hand side, we have
  `-y^2`. On the left side we have
  `5y^2` and
  `4y^2`, which is equal to
  `9y^2`. So we would need to subtract
  `10y^2` to make right hand side into
  `-y^2`.

Clearly Option B is right.