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

$$(y+2)(y-2)-(y-1)(y+5)$$

Evaluate

$$1-4y$$

Solution Steps

Consider \left(y+2\right)\left(y-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of y-1 by each term of y+5.

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

Combine 5y and -y to get 4y.

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

To find the opposite of y^{2}+4y-5, find the opposite of each term.

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

The opposite of -5 is 5.

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

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

$$-4-4y+5$$

Add -4 and 5 to get 1.

$$1-4y$$

Expand

$$1-4y$$

Solution Steps

Consider \left(y+2\right)\left(y-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

Apply the distributive property by multiplying each term of y-1 by each term of y+5.

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

Combine 5y and -y to get 4y.

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

To find the opposite of y^{2}+4y-5, find the opposite of each term.

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

The opposite of -5 is 5.

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

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

$$-4-4y+5$$

Add -4 and 5 to get 1.

$$1-4y$$