Question

How do you find the quotient of `(3x^2 + 4xy + 3xy + 4y^2) ÷ (x + y)`?

Answer 1

The remainder is `=0` and the quotient is `color(red)(=3x+4y`

Explanation:

`color(white)(aaaaaaa)` `color(red)(3x+4y`
`color(white)(aaaaaa)` `-----`
`color(white)(aaaaa)` `|` `3x^2+7xy +4y^2`
`color(white)(aaaaaaaaaaaa)` `3x^2+3xy`
`color(white)(aaaaaaaaaaaaa)` `0+4xy+4y^2`
`color(white)(aaaaaaaaaaaaaaaa)` `4xy+4y^2`
`color(white)(aaaaaaaaaaaaaaaaa)` `---`
`color(white)(aaaaaaaaaaaaaaaaaaa)` `0+0`

The remainder is `=0` and the quotient is `color(red)(=3x+4y`

Answer 2

`" The Quotient="(3x+4y).`

Explanation:

`ul(3x^2+4xy)+ul(3xy+4y^2),`

`=x(3x+4y)+y(3x+4y),`

`=(3x+4y)(x+y).`

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

`=(3x^2+4xy+3xy+4y^2)/(x+y),`

`={(3x+4y)(cancel(x+y))}/(cancel(x+y)),`

`=(3x+4y)," is the desired quotient."`

Enjoy Maths.!