Solve left(t^-1-3xright)left(t^-1+3xright)

$$\left( { t }^{ -1 } -3x \right) \left( { t }^{ -1 } +3x \right)$$

Evaluate

$$-9x^{2}+\frac{1}{t^{2}}$$

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}.

$$\left(t^{-1}\right)^{2}-\left(3x\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$t^{-2}-\left(3x\right)^{2}$$

Expand \left(3x\right)^{2}.

$$t^{-2}-3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$t^{-2}-9x^{2}$$

Expand

$$-9x^{2}+\frac{1}{t^{2}}$$

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}.

$$\left(t^{-1}\right)^{2}-\left(3x\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$t^{-2}-\left(3x\right)^{2}$$

Expand \left(3x\right)^{2}.

$$t^{-2}-3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$t^{-2}-9x^{2}$$