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

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

Expand

$$2x^{7}-30x^{5}+150x^{3}-250x$$

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}.

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

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

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

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

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

Use the distributive property to multiply 2x by x^{6}-15x^{4}+75x^{2}-125.

$$2x^{7}-30x^{5}+150x^{3}-250x$$

Evaluate

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

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}.

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

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

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

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

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

Use the distributive property to multiply 2x by x^{6}-15x^{4}+75x^{2}-125.

$$2x^{7}-30x^{5}+150x^{3}-250x$$