What is (x+5)^2-(x-5)^2-(x^2+7x-14) ?

The solution to (x+5)^2-(x-5)^2-(x^2+7x-14) is -x^2+13x+14

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simplify (x+5)^2-(x-5)^2-(x^2+7x-14)

simplify

(x + 5)^{2} - (x - 5)^{2} - (x^{2} + 7 x - 14)

- x^{2} + 13 x + 14

Solution steps

(x + 5)^{2} - (x - 5)^{2} - (x^{2} + 7 x - 14)

Apply the distributive law:

- (a + b) = - a - b

- (x^{2} + 7 x - 14) = - x^{2} - 7 x + 14

= (x + 5)^{2} - (x - 5)^{2} - x^{2} - 7 x + 14

Expand

(x + 5)^{2} : x^{2} + 10 x + 25

= x^{2} + 10 x + 25 - (x - 5)^{2} - x^{2} - 7 x + 14

Expand

- (x - 5)^{2} : - x^{2} + 10 x - 25

= x^{2} + 10 x + 25 - x^{2} + 10 x - 25 - x^{2} - 7 x + 14

Group like terms

= x^{2} - x^{2} - x^{2} + 10 x + 10 x - 7 x + 25 - 25 + 14

Add similar elements:

x^{2} - x^{2} - x^{2} = - x^{2}

= - x^{2} + 10 x + 10 x - 7 x + 25 - 25 + 14

Add similar elements:

10 x + 10 x - 7 x = 13 x

= - x^{2} + 13 x + 25 - 25 + 14

Add the numbers:

25 - 25 + 14 = 14

= - x^{2} + 13 x + 14

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What is (x+5)^2-(x-5)^2-(x^2+7x-14) ?
The solution to (x+5)^2-(x-5)^2-(x^2+7x-14) is -x^2+13x+14