Solve (x/5+6)(x/5-6)

$$( \frac { x } { 5 } + 6 ) ( \frac { x } { 5 } - 6 )$$

Evaluate

$$\frac{x^{2}}{25}-36$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{5}{5}.

$$\left(\frac{x}{5}+\frac{6\times 5}{5}\right)\left(\frac{x}{5}-6\right)$$

Since \frac{x}{5} and \frac{6\times 5}{5} have the same denominator, add them by adding their numerators.

$$\frac{x+6\times 5}{5}\left(\frac{x}{5}-6\right)$$

Do the multiplications in x+6\times 5.

$$\frac{x+30}{5}\left(\frac{x}{5}-6\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{5}{5}.

$$\frac{x+30}{5}\left(\frac{x}{5}-\frac{6\times 5}{5}\right)$$

Since \frac{x}{5} and \frac{6\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+30}{5}\times \frac{x-6\times 5}{5}$$

Do the multiplications in x-6\times 5.

$$\frac{x+30}{5}\times \frac{x-30}{5}$$

Multiply \frac{x+30}{5} times \frac{x-30}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+30\right)\left(x-30\right)}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{\left(x+30\right)\left(x-30\right)}{25}$$

Consider \left(x+30\right)\left(x-30\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{x^{2}-30^{2}}{25}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{x^{2}-900}{25}$$

Expand

$$\frac{x^{2}}{25}-36$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{5}{5}.

$$\left(\frac{x}{5}+\frac{6\times 5}{5}\right)\left(\frac{x}{5}-6\right)$$

Since \frac{x}{5} and \frac{6\times 5}{5} have the same denominator, add them by adding their numerators.

$$\frac{x+6\times 5}{5}\left(\frac{x}{5}-6\right)$$

Do the multiplications in x+6\times 5.

$$\frac{x+30}{5}\left(\frac{x}{5}-6\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{5}{5}.

$$\frac{x+30}{5}\left(\frac{x}{5}-\frac{6\times 5}{5}\right)$$

Since \frac{x}{5} and \frac{6\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+30}{5}\times \frac{x-6\times 5}{5}$$

Do the multiplications in x-6\times 5.

$$\frac{x+30}{5}\times \frac{x-30}{5}$$

Multiply \frac{x+30}{5} times \frac{x-30}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+30\right)\left(x-30\right)}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{\left(x+30\right)\left(x-30\right)}{25}$$

Consider \left(x+30\right)\left(x-30\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{x^{2}-30^{2}}{25}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{x^{2}-900}{25}$$