What is 64(a+2b)^3-343(a-2b)^3 ?

The solution to 64(a+2b)^3-343(a-2b)^3 is -279a^3+2442a^2b-3348ab^2+3256b^3

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simplify 64(a+2b)^3-343(a-2b)^3

simplify

64 (a + 2 b)^{3} - 343 (a - 2 b)^{3}

- 279 a^{3} + 2442 a^{2} b - 3348 a b^{2} + 3256 b^{3}

Solution steps

64 (a + 2 b)^{3} - 343 (a - 2 b)^{3}

Expand

64 (a + 2 b)^{3} : 64 a^{3} + 384 a^{2} b + 768 a b^{2} + 512 b^{3}

= 64 a^{3} + 384 a^{2} b + 768 a b^{2} + 512 b^{3} - 343 (a - 2 b)^{3}

Expand

- 343 (a - 2 b)^{3} : - 343 a^{3} + 2058 a^{2} b - 4116 a b^{2} + 2744 b^{3}

= 64 a^{3} + 384 a^{2} b + 768 a b^{2} + 512 b^{3} - 343 a^{3} + 2058 a^{2} b - 4116 a b^{2} + 2744 b^{3}

Group like terms

= 64 a^{3} - 343 a^{3} + 384 a^{2} b + 2058 a^{2} b + 768 a b^{2} - 4116 a b^{2} + 512 b^{3} + 2744 b^{3}

Add similar elements:

64 a^{3} - 343 a^{3} = - 279 a^{3}

= - 279 a^{3} + 384 a^{2} b + 2058 a^{2} b + 768 a b^{2} - 4116 a b^{2} + 512 b^{3} + 2744 b^{3}

Add similar elements:

384 a^{2} b + 2058 a^{2} b = 2442 a^{2} b

= - 279 a^{3} + 2442 a^{2} b + 768 a b^{2} - 4116 a b^{2} + 512 b^{3} + 2744 b^{3}

Add similar elements:

768 a b^{2} - 4116 a b^{2} = - 3348 a b^{2}

= - 279 a^{3} + 2442 a^{2} b - 3348 a b^{2} + 512 b^{3} + 2744 b^{3}

Add similar elements:

512 b^{3} + 2744 b^{3} = 3256 b^{3}

= - 279 a^{3} + 2442 a^{2} b - 3348 a b^{2} + 3256 b^{3}

x^{4} + 5 x^{2} + 9

\frac{\frac{( 2 x )}{5}}{\frac{12}{15}}

4 x \cdot 48 x

(\frac{1}{3} x - \frac{2}{3} y)^{3}

13 x - 4 - 2 x - 3 + 7

What is 64(a+2b)^3-343(a-2b)^3 ?
The solution to 64(a+2b)^3-343(a-2b)^3 is -279a^3+2442a^2b-3348ab^2+3256b^3