What is (2x+3)^2-(2x-3)^2+(3x-4)^2-8x^2-16 ?

The solution to (2x+3)^2-(2x-3)^2+(3x-4)^2-8x^2-16 is x^2

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simplify (2x+3)^2-(2x-3)^2+(3x-4)^2-8x^2-16

simplify

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

x^{2}

Solution steps

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

Expand

(2 x + 3)^{2} : 4 x^{2} + 12 x + 9

= 4 x^{2} + 12 x + 9 - (2 x - 3)^{2} + (3 x - 4)^{2} - 8 x^{2} - 16

Expand

- (2 x - 3)^{2} : - 4 x^{2} + 12 x - 9

= 4 x^{2} + 12 x + 9 - 4 x^{2} + 12 x - 9 + (3 x - 4)^{2} - 8 x^{2} - 16

Expand

(3 x - 4)^{2} : 9 x^{2} - 24 x + 16

= 4 x^{2} + 12 x + 9 - 4 x^{2} + 12 x - 9 + 9 x^{2} - 24 x + 16 - 8 x^{2} - 16

Group like terms

= 4 x^{2} - 4 x^{2} + 9 x^{2} - 8 x^{2} + 12 x + 12 x - 24 x + 9 - 9 + 16 - 16

Add similar elements:

4 x^{2} - 4 x^{2} + 9 x^{2} - 8 x^{2} = x^{2}

= x^{2} + 12 x + 12 x - 24 x + 9 - 9 + 16 - 16

Add similar elements:

12 x + 12 x - 24 x = 0

= x^{2} + 9 - 9 + 16 - 16

Add the numbers:

9 - 9 + 16 - 16 = 0

= x^{2}

\frac{3}{2} \cdot \frac{5}{2}

12 x^{2} - 8 x y - 15 y^{2}

\frac{5 x - 10}{3} \cdot \frac{12}{x - 2}

2 x^{2} + x - 36

512 - 227

What is (2x+3)^2-(2x-3)^2+(3x-4)^2-8x^2-16 ?
The solution to (2x+3)^2-(2x-3)^2+(3x-4)^2-8x^2-16 is x^2