Solve (x^2-5)^3-(-4x^3-5x)

$$( x ^ { 2 } - 5 ) ^ { 3 } - ( - 4 x ^ { 3 } - 5 x )$$

Evaluate

$$\left(x^{2}-5\right)^{3}+4x^{3}+5x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{2}-5\right)^{3}.

$$\left(x^{2}\right)^{3}-15\left(x^{2}\right)^{2}+75x^{2}-125-\left(-4x^{3}-5x\right)$$

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

$$x^{6}-15\left(x^{2}\right)^{2}+75x^{2}-125-\left(-4x^{3}-5x\right)$$

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

$$x^{6}-15x^{4}+75x^{2}-125-\left(-4x^{3}-5x\right)$$

To find the opposite of -4x^{3}-5x, find the opposite of each term.

$$x^{6}-15x^{4}+75x^{2}-125+4x^{3}+5x$$

Expand

$$x^{6}-15x^{4}+4x^{3}+75x^{2}+5x-125$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{2}-5\right)^{3}.

$$\left(x^{2}\right)^{3}-15\left(x^{2}\right)^{2}+75x^{2}-125-\left(-4x^{3}-5x\right)$$

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

$$x^{6}-15\left(x^{2}\right)^{2}+75x^{2}-125-\left(-4x^{3}-5x\right)$$

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

$$x^{6}-15x^{4}+75x^{2}-125-\left(-4x^{3}-5x\right)$$

To find the opposite of -4x^{3}-5x, find the opposite of each term.

$$x^{6}-15x^{4}+75x^{2}-125+4x^{3}+5x$$