Solve (a+1/2b)(a-1/2b)

$$( a + \frac { 1 } { 2 } b ) ( a - \frac { 1 } { 2 } b )$$

Evaluate

$$-\frac{b^{2}}{4}+a^{2}$$

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}.

$$a^{2}-\left(\frac{1}{2}b\right)^{2}$$

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

$$a^{2}-\left(\frac{1}{2}\right)^{2}b^{2}$$

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

$$a^{2}-\frac{1}{4}b^{2}$$

Expand

$$-\frac{b^{2}}{4}+a^{2}$$

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}.

$$a^{2}-\left(\frac{1}{2}b\right)^{2}$$

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

$$a^{2}-\left(\frac{1}{2}\right)^{2}b^{2}$$

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

$$a^{2}-\frac{1}{4}b^{2}$$