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

The required expression is 2y² - 4y + 5.

Step-by-step explanation:

We have to find the sum of first 2 expressions and then subtracting an expression, let us consider a, to give the third expression. We have to find a.

y² + 5y - 1 + 3y² - 2y + 4

We have to group the like terms and doing the addition as,

= y² + 3y² + 5y - 2y - 1 + 4

= 4y² + 3y + 3

Now we have to subtract an expression a from the above sum to get the third expression.

4y² + 3y + 3 - a = 2y² + 7y - 2

Now we have to group the terms as,

a = 4y² + 3y + 3 - (2y² + 7y - 2)

= 4y² + 3y + 3 - 2y² - 7y + 2

Rearranging the terms as,

a = 4y² - 2y² + 3y - 7y + 3 + 2

= 2y² - 4y + 5

So the required expression is 2y² - 4y + 5.