Solve (1+x/6)(1-x/6)

$$(1+ \frac{ x }{ 6 } )(1- \frac{ x }{ 6 } )$$

Evaluate

$$-\frac{x^{2}}{36}+1$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6}{6}.

$$\left(\frac{6}{6}+\frac{x}{6}\right)\left(1-\frac{x}{6}\right)$$

Since \frac{6}{6} and \frac{x}{6} have the same denominator, add them by adding their numerators.

$$\frac{6+x}{6}\left(1-\frac{x}{6}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6}{6}.

$$\frac{6+x}{6}\left(\frac{6}{6}-\frac{x}{6}\right)$$

Since \frac{6}{6} and \frac{x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6+x}{6}\times \frac{6-x}{6}$$

Multiply \frac{6+x}{6} times \frac{6-x}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(6+x\right)\left(6-x\right)}{6\times 6}$$

Multiply 6 and 6 to get 36.

$$\frac{\left(6+x\right)\left(6-x\right)}{36}$$

Consider \left(6+x\right)\left(6-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{6^{2}-x^{2}}{36}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36-x^{2}}{36}$$

Expand

$$-\frac{x^{2}}{36}+1$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6}{6}.

$$\left(\frac{6}{6}+\frac{x}{6}\right)\left(1-\frac{x}{6}\right)$$

Since \frac{6}{6} and \frac{x}{6} have the same denominator, add them by adding their numerators.

$$\frac{6+x}{6}\left(1-\frac{x}{6}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6}{6}.

$$\frac{6+x}{6}\left(\frac{6}{6}-\frac{x}{6}\right)$$

Since \frac{6}{6} and \frac{x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6+x}{6}\times \frac{6-x}{6}$$

Multiply \frac{6+x}{6} times \frac{6-x}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(6+x\right)\left(6-x\right)}{6\times 6}$$

Multiply 6 and 6 to get 36.

$$\frac{\left(6+x\right)\left(6-x\right)}{36}$$

Consider \left(6+x\right)\left(6-x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{6^{2}-x^{2}}{36}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36-x^{2}}{36}$$