Solve y^2*(y^2-2y+3)*(y+2)^2=

$$y ^ { 2 } \cdot ( y ^ { 2 } - 2 y + 3 ) \cdot ( y + 2 ) ^ { 2 } =$$

Evaluate

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

Solution Steps

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

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

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

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

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

$$y^{6}+2y^{5}-y^{4}+4y^{3}+12y^{2}$$

Expand

$$y^{6}+2y^{5}-y^{4}+4y^{3}+12y^{2}$$

Solution Steps

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

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

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

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

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

$$y^{6}+2y^{5}-y^{4}+4y^{3}+12y^{2}$$