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

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

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}.

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

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

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

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

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

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}.

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

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

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

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

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