Solve 3s^2(3s-9s^2)^2

$$3 s ^ { 2 } ( 3 s - 9 s ^ { 2 } ) ^ { 2 }$$

Evaluate

$$27\left(1-3s\right)^{2}s^{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3s-9s^{2}\right)^{2}.

$$3s^{2}\left(9s^{2}-54ss^{2}+81\left(s^{2}\right)^{2}\right)$$

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

$$3s^{2}\left(9s^{2}-54s^{3}+81\left(s^{2}\right)^{2}\right)$$

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

$$3s^{2}\left(9s^{2}-54s^{3}+81s^{4}\right)$$

Use the distributive property to multiply 3s^{2} by 9s^{2}-54s^{3}+81s^{4}.

$$27s^{4}-162s^{5}+243s^{6}$$

Expand

$$243s^{6}-162s^{5}+27s^{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3s-9s^{2}\right)^{2}.

$$3s^{2}\left(9s^{2}-54ss^{2}+81\left(s^{2}\right)^{2}\right)$$

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

$$3s^{2}\left(9s^{2}-54s^{3}+81\left(s^{2}\right)^{2}\right)$$

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

$$3s^{2}\left(9s^{2}-54s^{3}+81s^{4}\right)$$

Use the distributive property to multiply 3s^{2} by 9s^{2}-54s^{3}+81s^{4}.

$$27s^{4}-162s^{5}+243s^{6}$$