Solve 2y^{4}+y^{3}+3y^{4}(y^{3}-3y^4+2y^2)(9y^3-3y^2-6y)

$$2 y ^ { 4 } + y ^ { 3 } + 3 y ^ { 4 } ( y ^ { 3 } - 3 y ^ { 4 } + 2 y ^ { 2 } ) ( 9 y ^ { 3 } - 3 y ^ { 2 } - 6 y )$$

Evaluate

$$y^{3}\left(1+2y-36y^{4}-36y^{5}+99y^{6}+54y^{7}-81y^{8}\right)$$

Solution Steps

Use the distributive property to multiply 3y^{4} by y^{3}-3y^{4}+2y^{2}.

$$2y^{4}+y^{3}+\left(3y^{7}-9y^{8}+6y^{6}\right)\left(9y^{3}-3y^{2}-6y\right)$$

Use the distributive property to multiply 3y^{7}-9y^{8}+6y^{6} by 9y^{3}-3y^{2}-6y and combine like terms.

$$2y^{4}+y^{3}+54y^{10}+99y^{9}-36y^{8}-81y^{11}-36y^{7}$$

Expand

$$y^{3}+2y^{4}-36y^{7}-36y^{8}+99y^{9}+54y^{10}-81y^{11}$$

Solution Steps

Use the distributive property to multiply 3y^{4} by y^{3}-3y^{4}+2y^{2}.

$$2y^{4}+y^{3}+\left(3y^{7}-9y^{8}+6y^{6}\right)\left(9y^{3}-3y^{2}-6y\right)$$

Use the distributive property to multiply 3y^{7}-9y^{8}+6y^{6} by 9y^{3}-3y^{2}-6y and combine like terms.

$$2y^{4}+y^{3}+54y^{10}+99y^{9}-36y^{8}-81y^{11}-36y^{7}$$