Solve 2(y-1)^2+5(y-1)+3

$$2 ( y - 1 ) ^ { 2 } + 5 ( y - 1 ) + 3$$

Evaluate

$$y\left(2y+1\right)$$

Solution Steps

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

$$2\left(y^{2}-2y+1\right)+5\left(y-1\right)+3$$

Use the distributive property to multiply 2 by y^{2}-2y+1.

$$2y^{2}-4y+2+5\left(y-1\right)+3$$

Use the distributive property to multiply 5 by y-1.

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

Combine -4y and 5y to get y.

$$2y^{2}+y+2-5+3$$

Subtract 5 from 2 to get -3.

$$2y^{2}+y-3+3$$

Add -3 and 3 to get 0.

$$2y^{2}+y$$

Expand

$$2y^{2}+y$$

Solution Steps

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

$$2\left(y^{2}-2y+1\right)+5\left(y-1\right)+3$$

Use the distributive property to multiply 2 by y^{2}-2y+1.

$$2y^{2}-4y+2+5\left(y-1\right)+3$$

Use the distributive property to multiply 5 by y-1.

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

Combine -4y and 5y to get y.

$$2y^{2}+y+2-5+3$$

Subtract 5 from 2 to get -3.

$$2y^{2}+y-3+3$$

Add -3 and 3 to get 0.

$$2y^{2}+y$$