Solve (4p^2+7q)(4p^2-7q)

$$( 4 p ^ { 2 } + 7 q ) ( 4 p ^ { 2 } - 7 q )$$

Evaluate

$$16p^{4}-49q^{2}$$

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}.

$$\left(4p^{2}\right)^{2}-\left(7q\right)^{2}$$

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

$$4^{2}\left(p^{2}\right)^{2}-\left(7q\right)^{2}$$

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

$$4^{2}p^{4}-\left(7q\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16p^{4}-\left(7q\right)^{2}$$

Expand \left(7q\right)^{2}.

$$16p^{4}-7^{2}q^{2}$$

Calculate 7 to the power of 2 and get 49.

$$16p^{4}-49q^{2}$$

Expand

$$16p^{4}-49q^{2}$$

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}.

$$\left(4p^{2}\right)^{2}-\left(7q\right)^{2}$$

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

$$4^{2}\left(p^{2}\right)^{2}-\left(7q\right)^{2}$$

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

$$4^{2}p^{4}-\left(7q\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16p^{4}-\left(7q\right)^{2}$$

Expand \left(7q\right)^{2}.

$$16p^{4}-7^{2}q^{2}$$

Calculate 7 to the power of 2 and get 49.

$$16p^{4}-49q^{2}$$