Solve ((2p+9q^2)(2p-9q^2)

$$( ( 2 p + 9 q ^ { 2 } ) ( 2 p - 9 q ^ { 2 } )$$

Evaluate

$$4p^{2}-81q^{4}$$

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}.

$$\left(2p\right)^{2}-\left(9q^{2}\right)^{2}$$

Expand \left(2p\right)^{2}.

$$2^{2}p^{2}-\left(9q^{2}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4p^{2}-\left(9q^{2}\right)^{2}$$

Expand \left(9q^{2}\right)^{2}.

$$4p^{2}-9^{2}\left(q^{2}\right)^{2}$$

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

$$4p^{2}-9^{2}q^{4}$$

Calculate 9 to the power of 2 and get 81.

$$4p^{2}-81q^{4}$$

Expand

$$4p^{2}-81q^{4}$$

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}.

$$\left(2p\right)^{2}-\left(9q^{2}\right)^{2}$$

Expand \left(2p\right)^{2}.

$$2^{2}p^{2}-\left(9q^{2}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4p^{2}-\left(9q^{2}\right)^{2}$$

Expand \left(9q^{2}\right)^{2}.

$$4p^{2}-9^{2}\left(q^{2}\right)^{2}$$

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

$$4p^{2}-9^{2}q^{4}$$

Calculate 9 to the power of 2 and get 81.

$$4p^{2}-81q^{4}$$