What is (4a+3b)^3-(4a-3b)^3 ?

The solution to (4a+3b)^3-(4a-3b)^3 is 288a^2b+54b^3

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simplify (4a+3b)^3-(4a-3b)^3

simplify

(4 a + 3 b)^{3} - (4 a - 3 b)^{3}

288 a^{2} b + 54 b^{3}

Solution steps

(4 a + 3 b)^{3} - (4 a - 3 b)^{3}

Expand

(4 a + 3 b)^{3} : 64 a^{3} + 144 a^{2} b + 108 a b^{2} + 27 b^{3}

= 64 a^{3} + 144 a^{2} b + 108 a b^{2} + 27 b^{3} - (4 a - 3 b)^{3}

Expand

- (4 a - 3 b)^{3} : - 64 a^{3} + 144 a^{2} b - 108 a b^{2} + 27 b^{3}

= 64 a^{3} + 144 a^{2} b + 108 a b^{2} + 27 b^{3} - 64 a^{3} + 144 a^{2} b - 108 a b^{2} + 27 b^{3}

Group like terms

= 64 a^{3} - 64 a^{3} + 144 a^{2} b + 144 a^{2} b + 108 a b^{2} - 108 a b^{2} + 27 b^{3} + 27 b^{3}

Add similar elements:

64 a^{3} - 64 a^{3} = 0

= 144 a^{2} b + 144 a^{2} b + 108 a b^{2} - 108 a b^{2} + 27 b^{3} + 27 b^{3}

Add similar elements:

144 a^{2} b + 144 a^{2} b = 288 a^{2} b

= 288 a^{2} b + 108 a b^{2} - 108 a b^{2} + 27 b^{3} + 27 b^{3}

Add similar elements:

108 a b^{2} - 108 a b^{2} = 0

= 288 a^{2} b + 27 b^{3} + 27 b^{3}

Add similar elements:

27 b^{3} + 27 b^{3} = 54 b^{3}

= 288 a^{2} b + 54 b^{3}

3^{2} y^{4} z x^{3} y^{- 3} z^{2}

4 (1 - x^{3})^{3}

(a - b + c)^{2} + 2 (a - b + c) (b - c) + (b - c)^{2}

x (x^{2} - 1) (x + 2) - 8

k \cdot (\frac{- 3}{k})^{2} + 6 \cdot (\frac{- 3}{k}) - 3

What is (4a+3b)^3-(4a-3b)^3 ?
The solution to (4a+3b)^3-(4a-3b)^3 is 288a^2b+54b^3