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: $2y^2-4y+5$

Step-by-step 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:

$2y^2-4y+5$