Question

Match with the sum of the monomial and binomial. Tiles 2x2y + (x2y − 2xy2) (5xy2 − x2y) + 3x2y 4x2y + (x2y + xy2) x2y + (-2xy2 − 4x2y) Pairs 5xy2 + 2x2y -3x2y − 2xy2 3x2y − 2xy2 5x2y + xy2

Answer 1

`1.~ 2x^2y + (x^2y - 2xy^2) = 3x^2y - 2xy^2\\2.~(5xy^2 - x^2y) + 3x^2y=5xy^2 + 2x^2y\\3.~4x^2y +(x^2y +xy^2)= 5xy^2+ 2x^2y\\3.~4x^2y + (x^2y + xy^2)=5x^2y +xy^2\\4.~x^2y + (-2xy^2 - 4x^2y)=-3x^2y - 2xy^2`

Explanation:

We have to match the given monomials and binomials.

Monomials:

`2x^2y + (x^2y - 2xy^2)\\(5xy^2 - x^2y) + 3x^2y\\4x^2y + (x^2y + xy^2)\\x^2y + (-2xy^2 - 4x^2y)`

The given binomials are:

`5xy^2 + 2x^2y\\ -3x^2y - 2xy^2 \\3x^2y - 2xy^2\\ 5x^2y + xy^2`

Solving the monomials and matching can be done in the following manner:

`1.~ 2x^2y + (x^2y - 2xy^2)\\= 2x^2y + x^2y - 2xy^2 = 3x^2y - 2xy^2\\2.~(5xy^2 - x^2y) + 3x^2y\\=5xy^2 + 3x^2y - x^2y = 5xy^2 + 2x^2y\\3.~4x^2y + (x^2y + xy^2)\\= 4x^2y + x^2y + xy^2 = 5x^2y +xy^2\\4.~x^2y + (-2xy^2 - 4x^2y)\\= x^2y - 4x^2y-2xy^2 = -3x^2y - 2xy^2`

Answer 2

We will simply solve them and get correct answers that will match the answers provided.

1.
`2x^(2)y+(x^(2)y-2xy^(2) )`

=
`3x^(2) y-2xy^(2)`

2.
`(5xy^(2)-x^(2) y)+3x^(2) y`

=
`5xy^(2) +2x^(2) y`

3.
`4x^(2) y+(x^(2) y+xy^(2) )`

=
`5x^(2) y+xy^(2)`

4.
`x^(2) y+(-2xy^(2)-4x^(2) y)`

=
`-3x^(2) y-2xy^(2)`