Solve (2x^{2})^3-6x^3(x^3+2x^2+x)

$$( 2 x ^ { 2 } ) ^ { 3 } - 6 x ^ { 3 } ( x ^ { 3 } + 2 x ^ { 2 } + x )$$

Evaluate

$$-6\left(x+1\right)^{2}x^{4}+8x^{6}$$

Solution Steps

Expand \left(2x^{2}\right)^{3}.

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

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

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

Calculate 2 to the power of 3 and get 8.

$$8x^{6}-6x^{3}\left(x^{3}+2x^{2}+x\right)$$

Use the distributive property to multiply -6x^{3} by x^{3}+2x^{2}+x.

$$8x^{6}-6x^{6}-12x^{5}-6x^{4}$$

Combine 8x^{6} and -6x^{6} to get 2x^{6}.

$$2x^{6}-12x^{5}-6x^{4}$$

Expand

$$2x^{6}-12x^{5}-6x^{4}$$

Solution Steps

Expand \left(2x^{2}\right)^{3}.

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

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

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

Calculate 2 to the power of 3 and get 8.

$$8x^{6}-6x^{3}\left(x^{3}+2x^{2}+x\right)$$

Use the distributive property to multiply -6x^{3} by x^{3}+2x^{2}+x.

$$8x^{6}-6x^{6}-12x^{5}-6x^{4}$$

Combine 8x^{6} and -6x^{6} to get 2x^{6}.

$$2x^{6}-12x^{5}-6x^{4}$$