Solve (sqrt{5}-1)(sqrt{5}+1)-(-1/3)^-2-(11-2)^0

$$( \sqrt { 5 } - 1 ) ( \sqrt { 5 } + 1 ) - ( - \frac { 1 } { 3 } ) ^ { - 2 } - ( 11 - 2 ) ^ { 0 }$$

Evaluate

$$-6$$

Solution Steps

Consider \left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$\left(\sqrt{5}\right)^{2}-1-\left(-\frac{1}{3}\right)^{-2}-\left(11-2\right)^{0}$$

The square of \sqrt{5} is 5.

$$5-1-\left(-\frac{1}{3}\right)^{-2}-\left(11-2\right)^{0}$$

Subtract 1 from 5 to get 4.

$$4-\left(-\frac{1}{3}\right)^{-2}-\left(11-2\right)^{0}$$

Calculate -\frac{1}{3} to the power of -2 and get 9.

$$4-9-\left(11-2\right)^{0}$$

Subtract 9 from 4 to get -5.

$$-5-\left(11-2\right)^{0}$$

Subtract 2 from 11 to get 9.

$$-5-9^{0}$$

Calculate 9 to the power of 0 and get 1.

$$-5-1$$

Subtract 1 from -5 to get -6.

$$-6$$

Factor

$$-6$$