Solve f(x)=(x^3+x^2)^3

$$f ( x ) = ( x ^ { 3 } + x ^ { 2 } ) ^ { 3 }$$

Evaluate

$$\left(x+1\right)^{3}x^{6}$$

Solution Steps

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

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

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

$$x^{9}+3\left(x^{3}\right)^{2}x^{2}+3x^{3}\left(x^{2}\right)^{2}+\left(x^{2}\right)^{3}$$

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

$$x^{9}+3x^{6}x^{2}+3x^{3}\left(x^{2}\right)^{2}+\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

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

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

$$x^{9}+3x^{8}+3x^{3}x^{4}+\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{9}+3x^{8}+3x^{7}+\left(x^{2}\right)^{3}$$

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

$$x^{9}+3x^{8}+3x^{7}+x^{6}$$

Expand

$$x^{9}+3x^{8}+3x^{7}+x^{6}$$

Solution Steps

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

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

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

$$x^{9}+3\left(x^{3}\right)^{2}x^{2}+3x^{3}\left(x^{2}\right)^{2}+\left(x^{2}\right)^{3}$$

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

$$x^{9}+3x^{6}x^{2}+3x^{3}\left(x^{2}\right)^{2}+\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

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

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

$$x^{9}+3x^{8}+3x^{3}x^{4}+\left(x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{9}+3x^{8}+3x^{7}+\left(x^{2}\right)^{3}$$

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

$$x^{9}+3x^{8}+3x^{7}+x^{6}$$