Solve (3s+13)^3*(2s)^2

$$( 3 s + 13 ) ^ { 3 } \cdot ( 2 s ) ^ { 2 }$$

Evaluate

$$4s^{2}\left(3s+13\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(3s+13\right)^{3}.

$$\left(27s^{3}+351s^{2}+1521s+2197\right)\times \left(2s\right)^{2}$$

Expand \left(2s\right)^{2}.

$$\left(27s^{3}+351s^{2}+1521s+2197\right)\times 2^{2}s^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\left(27s^{3}+351s^{2}+1521s+2197\right)\times 4s^{2}$$

Use the distributive property to multiply 27s^{3}+351s^{2}+1521s+2197 by 4.

$$\left(108s^{3}+1404s^{2}+6084s+8788\right)s^{2}$$

Use the distributive property to multiply 108s^{3}+1404s^{2}+6084s+8788 by s^{2}.

$$108s^{5}+1404s^{4}+6084s^{3}+8788s^{2}$$

Expand

$$108s^{5}+1404s^{4}+6084s^{3}+8788s^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(3s+13\right)^{3}.

$$\left(27s^{3}+351s^{2}+1521s+2197\right)\times \left(2s\right)^{2}$$

Expand \left(2s\right)^{2}.

$$\left(27s^{3}+351s^{2}+1521s+2197\right)\times 2^{2}s^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\left(27s^{3}+351s^{2}+1521s+2197\right)\times 4s^{2}$$

Use the distributive property to multiply 27s^{3}+351s^{2}+1521s+2197 by 4.

$$\left(108s^{3}+1404s^{2}+6084s+8788\right)s^{2}$$

Use the distributive property to multiply 108s^{3}+1404s^{2}+6084s+8788 by s^{2}.

$$108s^{5}+1404s^{4}+6084s^{3}+8788s^{2}$$