Solve (10sqrt{6}+3)(10sqrt{6}-3)=

$$( 10 \sqrt { 6 } + 3 ) ( 10 \sqrt { 6 } - 3 ) =$$

Evaluate

$$591$$

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}.

$$\left(10\sqrt{6}\right)^{2}-3^{2}$$

Expand \left(10\sqrt{6}\right)^{2}.

$$10^{2}\left(\sqrt{6}\right)^{2}-3^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100\left(\sqrt{6}\right)^{2}-3^{2}$$

The square of \sqrt{6} is 6.

$$100\times 6-3^{2}$$

Multiply 100 and 6 to get 600.

$$600-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$600-9$$

Subtract 9 from 600 to get 591.

$$591$$

Factor

$$3\times 197$$