Solve (x^3+4)^2-10(x^3+4)+24

$$( x ^ { 3 } + 4 ) ^ { 2 } - 10 ( x ^ { 3 } + 4 ) + 24$$

Evaluate

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

Solution Steps

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

$$\left(x^{3}\right)^{2}+8x^{3}+16-10\left(x^{3}+4\right)+24$$

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

$$x^{6}+8x^{3}+16-10\left(x^{3}+4\right)+24$$

Use the distributive property to multiply -10 by x^{3}+4.

$$x^{6}+8x^{3}+16-10x^{3}-40+24$$

Combine 8x^{3} and -10x^{3} to get -2x^{3}.

$$x^{6}-2x^{3}+16-40+24$$

Subtract 40 from 16 to get -24.

$$x^{6}-2x^{3}-24+24$$

Add -24 and 24 to get 0.

$$x^{6}-2x^{3}$$

Expand

$$x^{6}-2x^{3}$$

Solution Steps

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

$$\left(x^{3}\right)^{2}+8x^{3}+16-10\left(x^{3}+4\right)+24$$

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

$$x^{6}+8x^{3}+16-10\left(x^{3}+4\right)+24$$

Use the distributive property to multiply -10 by x^{3}+4.

$$x^{6}+8x^{3}+16-10x^{3}-40+24$$

Combine 8x^{3} and -10x^{3} to get -2x^{3}.

$$x^{6}-2x^{3}+16-40+24$$

Subtract 40 from 16 to get -24.

$$x^{6}-2x^{3}-24+24$$

Add -24 and 24 to get 0.

$$x^{6}-2x^{3}$$