Question

What algebraic expression must be subtracted from y2+5y-1 and 3y2-2y+4 to give you the sum of 2y2+7y-2

Answer 1

Answer:
`2y^2-4y+5`

Explanation:

The complete exercise is: "What algebraic expression must be subtracted from the sum of
`y^2 + 5y - 1` and
`3y^2-2y + 4` to give
`2y^2 + 7y-2` as the result?"

For this exercise it is necessary to remember that a sum is the result of an addition. Then, if you need to find the sum of
`y^2 + 5y - 1` and
`3y^2-2y + 4` , you need to add them by combining the like terms.

You also need to remember the multiplication of signs:

`(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-`

So, you get that the sum of those expression is the following:

`(y^2 + 5y - 1)+(3y^2-2y + 4)=y^2 + 5y - 1+3y^2-2y + 4=4y^2+3y+3`

Since you must find the algebraic expression asked in the exercise, you need to subtract the expression
`2y^2 + 7y-2` from that sum calculated above.

Therefore, you get:

`(4y^2+3y+3)-(2y^2 + 7y-2)=4y^2+3y+3-2y^2- 7y+2=2y^2-4y+5`

Then, the algebraic expression asked is:

`2y^2-4y+5`