Solve (1/2x-y)(1/2x+y)

$$( \frac { 1 } { 2 } x - y ) ( \frac { 1 } { 2 } x + y )$$

Evaluate

$$\frac{x^{2}}{4}-y^{2}$$

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}.

$$\left(\frac{1}{2}x\right)^{2}-y^{2}$$

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

$$\left(\frac{1}{2}\right)^{2}x^{2}-y^{2}$$

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

$$\frac{1}{4}x^{2}-y^{2}$$

Expand

$$\frac{x^{2}}{4}-y^{2}$$

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}.

$$\left(\frac{1}{2}x\right)^{2}-y^{2}$$

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

$$\left(\frac{1}{2}\right)^{2}x^{2}-y^{2}$$

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

$$\frac{1}{4}x^{2}-y^{2}$$