What is 16(x+y)^2-25(x-2y)^2 ?

The solution to 16(x+y)^2-25(x-2y)^2 is -9x^2+132xy-84y^2

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simplify 16(x+y)^2-25(x-2y)^2

simplify

16 (x + y)^{2} - 25 (x - 2 y)^{2}

- 9 x^{2} + 132 x y - 84 y^{2}

Solution steps

16 (x + y)^{2} - 25 (x - 2 y)^{2}

Expand

16 (x + y)^{2} : 16 x^{2} + 32 x y + 16 y^{2}

= 16 x^{2} + 32 x y + 16 y^{2} - 25 (x - 2 y)^{2}

Expand

- 25 (x - 2 y)^{2} : - 25 x^{2} + 100 x y - 100 y^{2}

= 16 x^{2} + 32 x y + 16 y^{2} - 25 x^{2} + 100 x y - 100 y^{2}

Group like terms

= 16 x^{2} - 25 x^{2} + 32 x y + 100 x y + 16 y^{2} - 100 y^{2}

Add similar elements:

16 x^{2} - 25 x^{2} = - 9 x^{2}

= - 9 x^{2} + 32 x y + 100 x y + 16 y^{2} - 100 y^{2}

Add similar elements:

32 x y + 100 x y = 132 x y

= - 9 x^{2} + 132 x y + 16 y^{2} - 100 y^{2}

Add similar elements:

16 y^{2} - 100 y^{2} = - 84 y^{2}

= - 9 x^{2} + 132 x y - 84 y^{2}

\frac{4 a ^{16} + 2 b - 8}{2 ab}

\frac{8 x + 4}{2 x ^{2} - 5 x - 3}

\frac{6}{3 - 1}

8 y - 9 y

2 (5) (- 3) (- 2)

What is 16(x+y)^2-25(x-2y)^2 ?
The solution to 16(x+y)^2-25(x-2y)^2 is -9x^2+132xy-84y^2