Solve (3sqrt{5}+sqrt{2})(3sqrt{5}-sqrt{2})

$$( 3 \sqrt { 5 } + \sqrt { 2 } ) ( 3 \sqrt { 5 } - \sqrt { 2 } )$$

Evaluate

$$43$$

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}.

$$\left(3\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}$$

Expand \left(3\sqrt{5}\right)^{2}.

$$3^{2}\left(\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{5} is 5.

$$9\times 5-\left(\sqrt{2}\right)^{2}$$

Multiply 9 and 5 to get 45.

$$45-\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$45-2$$

Subtract 2 from 45 to get 43.

$$43$$

Factor

$$43$$