Question

Consider the following expression and the simplified expression. Expression Simplified Expression 3 x squared + 5 y squared box + 3 box + 4 y squared + 6 9 x squared minus y squared + 9 Which terms could be in the boxes to make the expressions equivalent? Positive 6 x squared and Negative 6 y squared Positive 6 x squared and Negative 10 y squared Positive 9 x squared and Negative 10 y squared Positive 9 x squared and Negative 6 y squared

Answer 1

Answer:

The correct answer is:

$+6x^{2}\\-9y^2$

Step-by-step explanation:

We are given the term:

$3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6 = 9x^{2} -y^{2} +9$

We have to fill in to the empty spaces such that the above equation gets satisfied.

First of all, let us simplify the LHS (Left Hand Side):

$3x^{2} +5y^{2} [\text{ \ }] +3 [\text{ \ }] +4y^{2} +6\\\Rightarrow 3x^{2} +5y^{2} +4y^{2} [\text{ \ }] [\text{ \ }] +6 +3\\\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9$

Now, let us equate the LHS and  RHS (Right Hand Side):

$\Rightarrow 3x^{2} +9y^{2} [\text{ \ }] [\text{ \ }] +9 = 9x^{2} -y^{2} +9$

Equating the coefficients of $x^{2}\ and\ y^{2}$ in LHS and RHS:

One box will have value = $9x^{2} -3x^{2} =+6x^{2}$

Other box will have value = $-y^{2} -9y^{2} =-10y^{2}$

The correct answer is:

$+6x^{2}\\-9y^2$

So, if we fill the boxes with above values, the expression will be simplified as given.

Answer 2

Answer:

The correct answer is B. Positive 6 x squared and Negative 10 y squared

Step-by-step explanation: