Question

Please help me with this.

Write the expression 8x^2y + 3xy^2 - 2xy - x^2y + 3xy - 5xy^2 in simplest form.
Then, answer the following questions using complete sentences:
a. How many terms are in the simplified expression?
b. How many of the terms in the simplified expression are positive?

Answer 1

`7x^(2) y-2xy^2+xy`

Three terms.

Two terms are positive.

Explanation:

`8x^2y + 3xy^2 - 2xy - x^2y + 3xy - 5xy^2`

Group like terms

`=8x^(2) y-x^(2) y+3xy^2-5xy^2-2xy+3xy`

Add similar elements:
`8x^(2) y-x^2y=7x^2y`

`=7x^2y+3xy^2-5xy^2-2xy+3xy`

Add similar elements:
`3xy^2-5xy^2=-2xy^2`

`=7x^(2) y-2xy^2-2xy+3xy`

Add similar elements:
`-2xy+3xy=xy`

`=7x^2y-2xy^2+xy`

`7x^2y` and
`-2xy^2` and
`xy` are the three different terms.

Only
`7x^2y` and
`xy` are positive terms, thus making two positive terms.