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

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

Evaluate

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

Solution Steps

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

$$125\left(x^{3}\right)^{3}+150\left(x^{3}\right)^{2}x+60x^{3}x^{2}+8x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$125x^{9}+150\left(x^{3}\right)^{2}x+60x^{3}x^{2}+8x^{3}$$

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

$$125x^{9}+150x^{6}x+60x^{3}x^{2}+8x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$125x^{9}+150x^{7}+60x^{3}x^{2}+8x^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$125x^{9}+150x^{7}+60x^{5}+8x^{3}$$

Expand

$$125x^{9}+150x^{7}+60x^{5}+8x^{3}$$

Solution Steps

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

$$125\left(x^{3}\right)^{3}+150\left(x^{3}\right)^{2}x+60x^{3}x^{2}+8x^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$125x^{9}+150\left(x^{3}\right)^{2}x+60x^{3}x^{2}+8x^{3}$$

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

$$125x^{9}+150x^{6}x+60x^{3}x^{2}+8x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$125x^{9}+150x^{7}+60x^{3}x^{2}+8x^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$125x^{9}+150x^{7}+60x^{5}+8x^{3}$$