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

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

Evaluate

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

Solution Steps

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

$$27\left(x^{4}\right)^{3}-54\left(x^{4}\right)^{2}x+36x^{4}x^{2}-8x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$27x^{12}-54\left(x^{4}\right)^{2}x+36x^{4}x^{2}-8x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$27x^{12}-54x^{8}x+36x^{4}x^{2}-8x^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$27x^{12}-54x^{9}+36x^{4}x^{2}-8x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$27x^{12}-54x^{9}+36x^{6}-8x^{3}$$

Expand

$$27x^{12}-54x^{9}+36x^{6}-8x^{3}$$

Solution Steps

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

$$27\left(x^{4}\right)^{3}-54\left(x^{4}\right)^{2}x+36x^{4}x^{2}-8x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$27x^{12}-54\left(x^{4}\right)^{2}x+36x^{4}x^{2}-8x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$27x^{12}-54x^{8}x+36x^{4}x^{2}-8x^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$27x^{12}-54x^{9}+36x^{4}x^{2}-8x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$27x^{12}-54x^{9}+36x^{6}-8x^{3}$$