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

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

Evaluate

$$-y^{2}+12y-14$$

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}.

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply -2 by y-1.

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

Apply the distributive property by multiplying each term of -2y+2 by each term of y-5.

$$y^{2}-4-2y^{2}+10y+2y-10$$

Combine 10y and 2y to get 12y.

$$y^{2}-4-2y^{2}+12y-10$$

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

$$-y^{2}-4+12y-10$$

Subtract 10 from -4 to get -14.

$$-y^{2}-14+12y$$

Expand

$$-y^{2}+12y-14$$

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}.

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply -2 by y-1.

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

Apply the distributive property by multiplying each term of -2y+2 by each term of y-5.

$$y^{2}-4-2y^{2}+10y+2y-10$$

Combine 10y and 2y to get 12y.

$$y^{2}-4-2y^{2}+12y-10$$

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

$$-y^{2}-4+12y-10$$

Subtract 10 from -4 to get -14.

$$-y^{2}-14+12y$$