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

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

Evaluate

$$-24y^{2}-30y-13$$

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}. Square 2.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5y+3\right)^{2}.

$$y^{2}-4-\left(25y^{2}+30y+9\right)$$

To find the opposite of 25y^{2}+30y+9, find the opposite of each term.

$$y^{2}-4-25y^{2}-30y-9$$

Combine y^{2} and -25y^{2} to get -24y^{2}.

$$-24y^{2}-4-30y-9$$

Subtract 9 from -4 to get -13.

$$-24y^{2}-13-30y$$

Expand

$$-24y^{2}-30y-13$$

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}. Square 2.

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5y+3\right)^{2}.

$$y^{2}-4-\left(25y^{2}+30y+9\right)$$

To find the opposite of 25y^{2}+30y+9, find the opposite of each term.

$$y^{2}-4-25y^{2}-30y-9$$

Combine y^{2} and -25y^{2} to get -24y^{2}.

$$-24y^{2}-4-30y-9$$

Subtract 9 from -4 to get -13.

$$-24y^{2}-13-30y$$