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

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

Evaluate

$$54a^{5}$$

Solution Steps

Combine a^{2} and 2a^{2} to get 3a^{2}.

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

Combine 3a^{2} and 3a^{2} to get 6a^{2}.

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

Multiply 3 and 6 to get 18.

$$18a^{2}a^{2}\left(a+2a\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$18a^{4}\left(a+2a\right)$$

Combine a and 2a to get 3a.

$$18a^{4}\times 3a$$

Multiply 18 and 3 to get 54.

$$54a^{4}a$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$54a^{5}$$

Expand

$$54a^{5}$$

Solution Steps

Combine a^{2} and 2a^{2} to get 3a^{2}.

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

Combine 3a^{2} and 3a^{2} to get 6a^{2}.

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

Multiply 3 and 6 to get 18.

$$18a^{2}a^{2}\left(a+2a\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$18a^{4}\left(a+2a\right)$$

Combine a and 2a to get 3a.

$$18a^{4}\times 3a$$

Multiply 18 and 3 to get 54.

$$54a^{4}a$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$54a^{5}$$