Solve (10m^2+8n^2)(10m^2-8n^2)=

$$( 10 m ^ { 2 } + 8 n ^ { 2 } ) ( 10 m ^ { 2 } - 8 n ^ { 2 } ) =$$

Evaluate

$$100m^{4}-64n^{4}$$

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}.

$$\left(10m^{2}\right)^{2}-\left(8n^{2}\right)^{2}$$

Expand \left(10m^{2}\right)^{2}.

$$10^{2}\left(m^{2}\right)^{2}-\left(8n^{2}\right)^{2}$$

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

$$10^{2}m^{4}-\left(8n^{2}\right)^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100m^{4}-\left(8n^{2}\right)^{2}$$

Expand \left(8n^{2}\right)^{2}.

$$100m^{4}-8^{2}\left(n^{2}\right)^{2}$$

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

$$100m^{4}-8^{2}n^{4}$$

Calculate 8 to the power of 2 and get 64.

$$100m^{4}-64n^{4}$$

Expand

$$100m^{4}-64n^{4}$$

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}.

$$\left(10m^{2}\right)^{2}-\left(8n^{2}\right)^{2}$$

Expand \left(10m^{2}\right)^{2}.

$$10^{2}\left(m^{2}\right)^{2}-\left(8n^{2}\right)^{2}$$

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

$$10^{2}m^{4}-\left(8n^{2}\right)^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100m^{4}-\left(8n^{2}\right)^{2}$$

Expand \left(8n^{2}\right)^{2}.

$$100m^{4}-8^{2}\left(n^{2}\right)^{2}$$

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

$$100m^{4}-8^{2}n^{4}$$

Calculate 8 to the power of 2 and get 64.

$$100m^{4}-64n^{4}$$