Solve (y^2+4y+1)^2(y+3y^2)

$$( y ^ { 2 } + 4 y + 1 ) ^ { 2 } ( y + 3 y ^ { 2 } )$$

Evaluate

$$y\left(3y+1\right)\left(y^{2}+4y+1\right)^{2}$$

Solution Steps

Square y^{2}+4y+1.

$$\left(y^{4}+8y^{3}+18y^{2}+8y+1\right)\left(y+3y^{2}\right)$$

Use the distributive property to multiply y^{4}+8y^{3}+18y^{2}+8y+1 by y+3y^{2} and combine like terms.

$$25y^{5}+3y^{6}+62y^{4}+42y^{3}+11y^{2}+y$$

Expand

$$3y^{6}+25y^{5}+62y^{4}+42y^{3}+11y^{2}+y$$

Solution Steps

Square y^{2}+4y+1.

$$\left(y^{4}+8y^{3}+18y^{2}+8y+1\right)\left(y+3y^{2}\right)$$

Use the distributive property to multiply y^{4}+8y^{3}+18y^{2}+8y+1 by y+3y^{2} and combine like terms.

$$25y^{5}+3y^{6}+62y^{4}+42y^{3}+11y^{2}+y$$