Question

How do you evaluate `(\frac { 3} { 4} x - \frac { 5} { 6} y ^ { 2} ) * (3/4x - 5/6 y^2)`?

Answer 1

`9/16x^2 + 10/8xy^2 + 25/36y^4`

Explanation:

You can use the grid method to make sure you multiply each thing by both things in the other bracket.

`3/4x * 3/4x = 9/16x^2`
`3/4x * 5/6y^2 = 5/8xy^2`
`5/6y^2 * 3/4x = 5/8xy^2`
`5/6y^2 * 5/6y^2 = 25/36y^4`

Then you can collect like terms and simplify your answer:
`9/16x^2 + 5/8xy^2 + 5/8xy^2 + 25/36y^4` =
`9/16x^2 + 10/8xy^2 + 25/36y^4`