Solve (3-4y)(3+4y)-(3+4y)^2

$$( 3 - 4 y ) ( 3 + 4 y ) - ( 3 + 4 y ) ^ { 2 }$$

Evaluate

$$-8y\left(4y+3\right)$$

Solution Steps

Consider \left(3-4y\right)\left(3+4y\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 3.

$$9-\left(4y\right)^{2}-\left(3+4y\right)^{2}$$

Expand \left(4y\right)^{2}.

$$9-4^{2}y^{2}-\left(3+4y\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$9-16y^{2}-\left(3+4y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+4y\right)^{2}.

$$9-16y^{2}-\left(9+24y+16y^{2}\right)$$

To find the opposite of 9+24y+16y^{2}, find the opposite of each term.

$$9-16y^{2}-9-24y-16y^{2}$$

Subtract 9 from 9 to get 0.

$$-16y^{2}-24y-16y^{2}$$

Combine -16y^{2} and -16y^{2} to get -32y^{2}.

$$-32y^{2}-24y$$

Expand

$$-32y^{2}-24y$$

Solution Steps

Consider \left(3-4y\right)\left(3+4y\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 3.

$$9-\left(4y\right)^{2}-\left(3+4y\right)^{2}$$

Expand \left(4y\right)^{2}.

$$9-4^{2}y^{2}-\left(3+4y\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$9-16y^{2}-\left(3+4y\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+4y\right)^{2}.

$$9-16y^{2}-\left(9+24y+16y^{2}\right)$$

To find the opposite of 9+24y+16y^{2}, find the opposite of each term.

$$9-16y^{2}-9-24y-16y^{2}$$

Subtract 9 from 9 to get 0.

$$-16y^{2}-24y-16y^{2}$$

Combine -16y^{2} and -16y^{2} to get -32y^{2}.

$$-32y^{2}-24y$$