Solve (a^2+5a)^2

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

Evaluate

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

Solution Steps

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

$$\left(a^{2}\right)^{2}+10a^{2}a+25a^{2}$$

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

$$a^{4}+10a^{2}a+25a^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{4}+10a^{3}+25a^{2}$$

Expand

$$a^{4}+10a^{3}+25a^{2}$$

Solution Steps

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

$$\left(a^{2}\right)^{2}+10a^{2}a+25a^{2}$$

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

$$a^{4}+10a^{2}a+25a^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{4}+10a^{3}+25a^{2}$$