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

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

Evaluate

$$3y^{2}-5y+13$$

Solution Steps

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

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

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

$$4y^{2}-4y+1-\left(y^{2}+y-12\right)$$

To find the opposite of y^{2}+y-12, find the opposite of each term.

$$4y^{2}-4y+1-y^{2}-y+12$$

Combine 4y^{2} and -y^{2} to get 3y^{2}.

$$3y^{2}-4y+1-y+12$$

Combine -4y and -y to get -5y.

$$3y^{2}-5y+1+12$$

Add 1 and 12 to get 13.

$$3y^{2}-5y+13$$

Expand

$$3y^{2}-5y+13$$

Solution Steps

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

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

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

$$4y^{2}-4y+1-\left(y^{2}+y-12\right)$$

To find the opposite of y^{2}+y-12, find the opposite of each term.

$$4y^{2}-4y+1-y^{2}-y+12$$

Combine 4y^{2} and -y^{2} to get 3y^{2}.

$$3y^{2}-4y+1-y+12$$

Combine -4y and -y to get -5y.

$$3y^{2}-5y+1+12$$

Add 1 and 12 to get 13.

$$3y^{2}-5y+13$$