Solve (-1/15x^30-z)(-1/15x^30+z)=

$$( - \frac { 1 } { 15 } x ^ { 30 } - z ) ( - \frac { 1 } { 15 } x ^ { 30 } + z ) =$$

Evaluate

$$\frac{x^{60}}{225}-z^{2}$$

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}.

$$\left(-\frac{1}{15}x^{30}\right)^{2}-z^{2}$$

Expand \left(-\frac{1}{15}x^{30}\right)^{2}.

$$\left(-\frac{1}{15}\right)^{2}\left(x^{30}\right)^{2}-z^{2}$$

To raise a power to another power, multiply the exponents. Multiply 30 and 2 to get 60.

$$\left(-\frac{1}{15}\right)^{2}x^{60}-z^{2}$$

Calculate -\frac{1}{15} to the power of 2 and get \frac{1}{225}.

$$\frac{1}{225}x^{60}-z^{2}$$

Expand

$$\frac{x^{60}}{225}-z^{2}$$

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}.

$$\left(-\frac{1}{15}x^{30}\right)^{2}-z^{2}$$

Expand \left(-\frac{1}{15}x^{30}\right)^{2}.

$$\left(-\frac{1}{15}\right)^{2}\left(x^{30}\right)^{2}-z^{2}$$

To raise a power to another power, multiply the exponents. Multiply 30 and 2 to get 60.

$$\left(-\frac{1}{15}\right)^{2}x^{60}-z^{2}$$

Calculate -\frac{1}{15} to the power of 2 and get \frac{1}{225}.

$$\frac{1}{225}x^{60}-z^{2}$$