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

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

Evaluate

$$-8y^{2}-12y-5$$

Solution Steps

Consider \left(y+1\right)\left(y-1\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 1.

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

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

$$y^{2}-1-\left(9y^{2}+12y+4\right)$$

To find the opposite of 9y^{2}+12y+4, find the opposite of each term.

$$y^{2}-1-9y^{2}-12y-4$$

Combine y^{2} and -9y^{2} to get -8y^{2}.

$$-8y^{2}-1-12y-4$$

Subtract 4 from -1 to get -5.

$$-8y^{2}-5-12y$$

Expand

$$-8y^{2}-12y-5$$

Solution Steps

Consider \left(y+1\right)\left(y-1\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 1.

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

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

$$y^{2}-1-\left(9y^{2}+12y+4\right)$$

To find the opposite of 9y^{2}+12y+4, find the opposite of each term.

$$y^{2}-1-9y^{2}-12y-4$$

Combine y^{2} and -9y^{2} to get -8y^{2}.

$$-8y^{2}-1-12y-4$$

Subtract 4 from -1 to get -5.

$$-8y^{2}-5-12y$$