Solve 14(5x^3+1)^3

$$14 ( 5 x ^ { 3 } + 1 ) ^ { 3 }$$

Expand

$$1750x^{9}+1050x^{6}+210x^{3}+14$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(5x^{3}+1\right)^{3}.

$$14\left(125\left(x^{3}\right)^{3}+75\left(x^{3}\right)^{2}+15x^{3}+1\right)$$

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

$$14\left(125x^{9}+75\left(x^{3}\right)^{2}+15x^{3}+1\right)$$

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

$$14\left(125x^{9}+75x^{6}+15x^{3}+1\right)$$

Use the distributive property to multiply 14 by 125x^{9}+75x^{6}+15x^{3}+1.

$$1750x^{9}+1050x^{6}+210x^{3}+14$$

Evaluate

$$14\left(5x^{3}+1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(5x^{3}+1\right)^{3}.

$$14\left(125\left(x^{3}\right)^{3}+75\left(x^{3}\right)^{2}+15x^{3}+1\right)$$

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

$$14\left(125x^{9}+75\left(x^{3}\right)^{2}+15x^{3}+1\right)$$

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

$$14\left(125x^{9}+75x^{6}+15x^{3}+1\right)$$

Use the distributive property to multiply 14 by 125x^{9}+75x^{6}+15x^{3}+1.

$$1750x^{9}+1050x^{6}+210x^{3}+14$$