Solve (4x^3-8x^2)^3

$$( 4 x ^ { 3 } - 8 x ^ { 2 } ) ^ { 3 }$$

Evaluate

$$64\left(x-2\right)^{3}x^{6}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(4x^{3}-8x^{2}\right)^{3}.

$$64\left(x^{3}\right)^{3}-384\left(x^{3}\right)^{2}x^{2}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$64x^{9}-384\left(x^{3}\right)^{2}x^{2}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$64x^{9}-384x^{6}x^{2}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$64x^{9}-384x^{8}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$64x^{9}-384x^{8}+768x^{3}x^{4}-512\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$64x^{9}-384x^{8}+768x^{7}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$64x^{9}-384x^{8}+768x^{7}-512x^{6}$$

Expand

$$64x^{9}-384x^{8}+768x^{7}-512x^{6}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(4x^{3}-8x^{2}\right)^{3}.

$$64\left(x^{3}\right)^{3}-384\left(x^{3}\right)^{2}x^{2}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$64x^{9}-384\left(x^{3}\right)^{2}x^{2}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$64x^{9}-384x^{6}x^{2}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$64x^{9}-384x^{8}+768x^{3}\left(x^{2}\right)^{2}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$64x^{9}-384x^{8}+768x^{3}x^{4}-512\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$64x^{9}-384x^{8}+768x^{7}-512\left(x^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$64x^{9}-384x^{8}+768x^{7}-512x^{6}$$