What is (y-7)^2-(y-8)^2+2y ?

The solution to (y-7)^2-(y-8)^2+2y is 4y-15

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simplify (y-7)^2-(y-8)^2+2y

simplify

(y - 7)^{2} - (y - 8)^{2} + 2 y

4 y - 15

Solution steps

(y - 7)^{2} - (y - 8)^{2} + 2 y

Expand

(y - 7)^{2} : y^{2} - 14 y + 49

= y^{2} - 14 y + 49 - (y - 8)^{2} + 2 y

Expand

- (y - 8)^{2} : - y^{2} + 16 y - 64

= y^{2} - 14 y + 49 - y^{2} + 16 y - 64 + 2 y

Group like terms

= y^{2} - y^{2} - 14 y + 16 y + 2 y + 49 - 64

Add similar elements:

y^{2} - y^{2} = 0

= - 14 y + 16 y + 2 y + 49 - 64

Add similar elements:

- 14 y + 16 y + 2 y = 4 y

= 4 y + 49 - 64

Subtract the numbers:

49 - 64 = - 15

= 4 y - 15

(y - 5) (y + 9)

24 - 54

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- 5 x^{2} (- x^{2} - 3 x)