Solve [(-2y+3)-2]^2+(y+1)^2

$$[ ( - 2 y + 3 ) - 2 ] ^ { 2 } + ( y + 1 ) ^ { 2 }$$

Evaluate

$$5y^{2}-2y+2$$

Solution Steps

Subtract 2 from 3 to get 1.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-2y+1\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+1\right)^{2}.

$$4y^{2}-4y+1+y^{2}+2y+1$$

Combine 4y^{2} and y^{2} to get 5y^{2}.

$$5y^{2}-4y+1+2y+1$$

Combine -4y and 2y to get -2y.

$$5y^{2}-2y+1+1$$

Add 1 and 1 to get 2.

$$5y^{2}-2y+2$$

Expand

$$5y^{2}-2y+2$$

Solution Steps

Subtract 2 from 3 to get 1.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-2y+1\right)^{2}.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(y+1\right)^{2}.

$$4y^{2}-4y+1+y^{2}+2y+1$$

Combine 4y^{2} and y^{2} to get 5y^{2}.

$$5y^{2}-4y+1+2y+1$$

Combine -4y and 2y to get -2y.

$$5y^{2}-2y+1+1$$

Add 1 and 1 to get 2.

$$5y^{2}-2y+2$$