Question

If P = 3x^2 + xy - 5y^2, Q = 2x^2 - xy + 3y^2 and R = -6x^2 + 4xy -7y^2what is P + Q - R ?

Answer 1

To find what is P + Q - R

From the equation given

$\text{ p = 3x}^2+xy-5y^2$$\Q=2x^{2\text{ }}-xy+3y^2$$\R=-6x^2+4xy-7y^2$$\P+Q-R=3x^2+xy-5y^2+(2x^2-xy+3y^2)-(-6x^2+4xy-7y^2)$

Now we will simplify the equation by first opening the parentheses

Values of Q will remain the same even after opening the parenthesis because it's addition but for the values of R, the signs will be affected because it's a subtraction.

That is :

$3x^2+xy-5y^2+2x^2-xy+3y^2+6x^2-4xy+7y^2$

So the next is to rearrange them according to their powers

$3x^2+2x^2+6x^2+xy-xy-4xy-5y^2+3y^2+7y^2$

Then we will add or subtract variables that are the same accordingly(depending on their signs)

$11x^2-4xy+5y^2$

Therefore

$\P+Q-R=11x^2-4xy+5y^2$