Solve (5sqrt{7}+2sqrt{5})(5sqrt{7}-2sqrt{5})

$$( 5 \sqrt { 7 } + 2 \sqrt { 5 } ) ( 5 \sqrt { 7 } - 2 \sqrt { 5 } )$$

Evaluate

$$155$$

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}.

$$\left(5\sqrt{7}\right)^{2}-\left(2\sqrt{5}\right)^{2}$$

Expand \left(5\sqrt{7}\right)^{2}.

$$5^{2}\left(\sqrt{7}\right)^{2}-\left(2\sqrt{5}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{7}\right)^{2}-\left(2\sqrt{5}\right)^{2}$$

The square of \sqrt{7} is 7.

$$25\times 7-\left(2\sqrt{5}\right)^{2}$$

Multiply 25 and 7 to get 175.

$$175-\left(2\sqrt{5}\right)^{2}$$

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

$$175-2^{2}\left(\sqrt{5}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$175-4\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$175-4\times 5$$

Multiply 4 and 5 to get 20.

$$175-20$$

Subtract 20 from 175 to get 155.

$$155$$

Factor

$$5\times 31$$