Solve (3v^2-6u)(3v^2+6u)

$$( 3 v ^ { 2 } - 6 u ) ( 3 v ^ { 2 } + 6 u )$$

Evaluate

$$9\left(v^{4}-4u^{2}\right)$$

Solution Steps

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

$$\left(3v^{2}\right)^{2}-\left(6u\right)^{2}$$

Expand \left(3v^{2}\right)^{2}.

$$3^{2}\left(v^{2}\right)^{2}-\left(6u\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$3^{2}v^{4}-\left(6u\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9v^{4}-\left(6u\right)^{2}$$

Expand \left(6u\right)^{2}.

$$9v^{4}-6^{2}u^{2}$$

Calculate 6 to the power of 2 and get 36.

$$9v^{4}-36u^{2}$$

Expand

$$9v^{4}-36u^{2}$$

Solution Steps

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

$$\left(3v^{2}\right)^{2}-\left(6u\right)^{2}$$

Expand \left(3v^{2}\right)^{2}.

$$3^{2}\left(v^{2}\right)^{2}-\left(6u\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$3^{2}v^{4}-\left(6u\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9v^{4}-\left(6u\right)^{2}$$

Expand \left(6u\right)^{2}.

$$9v^{4}-6^{2}u^{2}$$

Calculate 6 to the power of 2 and get 36.

$$9v^{4}-36u^{2}$$