Solve (1/4m+n)(1/4m-n)

$$( \frac { 1 } { 4 } m + n ) ( \frac { 1 } { 4 } m - n )$$

Evaluate

$$\frac{m^{2}}{16}-n^{2}$$

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}.

$$\left(\frac{1}{4}m\right)^{2}-n^{2}$$

Expand \left(\frac{1}{4}m\right)^{2}.

$$\left(\frac{1}{4}\right)^{2}m^{2}-n^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}m^{2}-n^{2}$$

Expand

$$\frac{m^{2}}{16}-n^{2}$$

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}.

$$\left(\frac{1}{4}m\right)^{2}-n^{2}$$

Expand \left(\frac{1}{4}m\right)^{2}.

$$\left(\frac{1}{4}\right)^{2}m^{2}-n^{2}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{1}{16}m^{2}-n^{2}$$