What is 16(2a-b)^2-9(a+b)^2 ?

The solution to 16(2a-b)^2-9(a+b)^2 is 55a^2-82ab+7b^2

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simplify 16(2a-b)^2-9(a+b)^2

simplify

16 (2 a - b)^{2} - 9 (a + b)^{2}

55 a^{2} - 82 ab + 7 b^{2}

Solution steps

16 (2 a - b)^{2} - 9 (a + b)^{2}

Expand

16 (2 a - b)^{2} : 64 a^{2} - 64 ab + 16 b^{2}

= 64 a^{2} - 64 ab + 16 b^{2} - 9 (a + b)^{2}

Expand

- 9 (a + b)^{2} : - 9 a^{2} - 18 ab - 9 b^{2}

= 64 a^{2} - 64 ab + 16 b^{2} - 9 a^{2} - 18 ab - 9 b^{2}

Group like terms

= 64 a^{2} - 9 a^{2} - 64 ab - 18 ab + 16 b^{2} - 9 b^{2}

Add similar elements:

64 a^{2} - 9 a^{2} = 55 a^{2}

= 55 a^{2} - 64 ab - 18 ab + 16 b^{2} - 9 b^{2}

Add similar elements:

- 64 ab - 18 ab = - 82 ab

= 55 a^{2} - 82 ab + 16 b^{2} - 9 b^{2}

Add similar elements:

16 b^{2} - 9 b^{2} = 7 b^{2}

= 55 a^{2} - 82 ab + 7 b^{2}

\frac{\frac{r ^{9}}{( r ^{4} )}}{( r ^{2} )}

sin (\frac{( x + y )}{2})

12 x^{3} y^{2} - 36 x^{3} y - 48 x y^{2} + 144 x^{2} y

3 u^{3} - 4 u^{2} - 12 u + 16

\frac{7 ^{n} + 7 ^{n} - 1}{7 ^{n} + 1 - 7 ^{n}}

What is 16(2a-b)^2-9(a+b)^2 ?
The solution to 16(2a-b)^2-9(a+b)^2 is 55a^2-82ab+7b^2