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

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

Evaluate

$$5-10y$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.

$$y^{2}-6y+9-\left(y+2\right)^{2}$$

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

$$y^{2}-6y+9-\left(y^{2}+4y+4\right)$$

To find the opposite of y^{2}+4y+4, find the opposite of each term.

$$y^{2}-6y+9-y^{2}-4y-4$$

Combine y^{2} and -y^{2} to get 0.

$$-6y+9-4y-4$$

Combine -6y and -4y to get -10y.

$$-10y+9-4$$

Subtract 4 from 9 to get 5.

$$-10y+5$$

Expand

$$5-10y$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.

$$y^{2}-6y+9-\left(y+2\right)^{2}$$

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

$$y^{2}-6y+9-\left(y^{2}+4y+4\right)$$

To find the opposite of y^{2}+4y+4, find the opposite of each term.

$$y^{2}-6y+9-y^{2}-4y-4$$

Combine y^{2} and -y^{2} to get 0.

$$-6y+9-4y-4$$

Combine -6y and -4y to get -10y.

$$-10y+9-4$$

Subtract 4 from 9 to get 5.

$$-10y+5$$