What is (x+5)^2-(x+4)^2-(x-3)^2+(x-4)^2 ?

The solution to (x+5)^2-(x+4)^2-(x-3)^2+(x-4)^2 is 16

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simplify (x+5)^2-(x+4)^2-(x-3)^2+(x-4)^2

simplify

(x + 5)^{2} - (x + 4)^{2} - (x - 3)^{2} + (x - 4)^{2}

16

Solution steps

(x + 5)^{2} - (x + 4)^{2} - (x - 3)^{2} + (x - 4)^{2}

Expand

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

= x^{2} + 10 x + 25 - (x + 4)^{2} - (x - 3)^{2} + (x - 4)^{2}

Expand

- (x + 4)^{2} : - x^{2} - 8 x - 16

= x^{2} + 10 x + 25 - x^{2} - 8 x - 16 - (x - 3)^{2} + (x - 4)^{2}

Expand

- (x - 3)^{2} : - x^{2} + 6 x - 9

= x^{2} + 10 x + 25 - x^{2} - 8 x - 16 - x^{2} + 6 x - 9 + (x - 4)^{2}

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= x^{2} + 10 x + 25 - x^{2} - 8 x - 16 - x^{2} + 6 x - 9 + x^{2} - 8 x + 16

Group like terms

= x^{2} - x^{2} - x^{2} + x^{2} + 10 x - 8 x + 6 x - 8 x + 25 - 16 - 9 + 16

Add similar elements:

x^{2} - x^{2} - x^{2} + x^{2} = 0

= 10 x - 8 x + 6 x - 8 x + 25 - 16 - 9 + 16

Add similar elements:

10 x - 8 x + 6 x - 8 x = 0

= 25 - 16 - 9 + 16

Add the numbers:

25 - 16 - 9 + 16 = 16

= 16

(4 x - 8) (7 x + 9)

\frac{( 5 i ) ^{4}}{( 4 - 3 i ) ^{2}}

\frac{2 x + 3}{4} - \frac{x - 1}{2}

\frac{3 x ( 2 x 4 ^{3} )}{4}

What is (x+5)^2-(x+4)^2-(x-3)^2+(x-4)^2 ?
The solution to (x+5)^2-(x+4)^2-(x-3)^2+(x-4)^2 is 16