Solve left(x^3+4right)^2*-4x^3

$${ \left( { x }^{ 3 } +4 \right) }^{ 2 } \times -4 { x }^{ 3 }$$

Evaluate

$$-4x^{3}\left(x^{3}+4\right)^{2}$$

Solution Steps

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

$$\left(\left(x^{3}\right)^{2}+8x^{3}+16\right)\left(-4\right)x^{3}$$

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

$$\left(x^{6}+8x^{3}+16\right)\left(-4\right)x^{3}$$

Use the distributive property to multiply x^{6}+8x^{3}+16 by -4.

$$\left(-4x^{6}-32x^{3}-64\right)x^{3}$$

Use the distributive property to multiply -4x^{6}-32x^{3}-64 by x^{3}.

$$-4x^{9}-32x^{6}-64x^{3}$$

Expand

$$-4x^{9}-32x^{6}-64x^{3}$$

Solution Steps

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

$$\left(\left(x^{3}\right)^{2}+8x^{3}+16\right)\left(-4\right)x^{3}$$

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

$$\left(x^{6}+8x^{3}+16\right)\left(-4\right)x^{3}$$

Use the distributive property to multiply x^{6}+8x^{3}+16 by -4.

$$\left(-4x^{6}-32x^{3}-64\right)x^{3}$$

Use the distributive property to multiply -4x^{6}-32x^{3}-64 by x^{3}.

$$-4x^{9}-32x^{6}-64x^{3}$$