Solve (a^2+a^5)^3=

$$( a ^ { 2 } + a ^ { 5 } ) ^ { 3 } =$$

Evaluate

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

Solution Steps

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(a^{2}+a^{5}\right)^{3}.

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

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

$$a^{6}+3\left(a^{2}\right)^{2}a^{5}+3a^{2}\left(a^{5}\right)^{2}+\left(a^{5}\right)^{3}$$

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

$$a^{6}+3a^{4}a^{5}+3a^{2}\left(a^{5}\right)^{2}+\left(a^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$a^{6}+3a^{9}+3a^{2}\left(a^{5}\right)^{2}+\left(a^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$a^{6}+3a^{9}+3a^{2}a^{10}+\left(a^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$a^{6}+3a^{9}+3a^{12}+\left(a^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$a^{6}+3a^{9}+3a^{12}+a^{15}$$

Expand

$$a^{15}+3a^{12}+3a^{9}+a^{6}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(a^{2}+a^{5}\right)^{3}.

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

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

$$a^{6}+3\left(a^{2}\right)^{2}a^{5}+3a^{2}\left(a^{5}\right)^{2}+\left(a^{5}\right)^{3}$$

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

$$a^{6}+3a^{4}a^{5}+3a^{2}\left(a^{5}\right)^{2}+\left(a^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$a^{6}+3a^{9}+3a^{2}\left(a^{5}\right)^{2}+\left(a^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$a^{6}+3a^{9}+3a^{2}a^{10}+\left(a^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$a^{6}+3a^{9}+3a^{12}+\left(a^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$a^{6}+3a^{9}+3a^{12}+a^{15}$$