Solve (4m^2-2n)(4m^2+2n)

$$( 4 m ^ { 2 } - 2 n ) ( 4 m ^ { 2 } + 2 n )$$

Evaluate

$$16m^{4}-4n^{2}$$

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}.

$$\left(4m^{2}\right)^{2}-\left(2n\right)^{2}$$

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

$$4^{2}\left(m^{2}\right)^{2}-\left(2n\right)^{2}$$

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

$$4^{2}m^{4}-\left(2n\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16m^{4}-\left(2n\right)^{2}$$

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

$$16m^{4}-2^{2}n^{2}$$

Calculate 2 to the power of 2 and get 4.

$$16m^{4}-4n^{2}$$

Expand

$$16m^{4}-4n^{2}$$

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}.

$$\left(4m^{2}\right)^{2}-\left(2n\right)^{2}$$

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

$$4^{2}\left(m^{2}\right)^{2}-\left(2n\right)^{2}$$

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

$$4^{2}m^{4}-\left(2n\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16m^{4}-\left(2n\right)^{2}$$

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

$$16m^{4}-2^{2}n^{2}$$

Calculate 2 to the power of 2 and get 4.

$$16m^{4}-4n^{2}$$