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

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

Evaluate

$$3$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{7}\right)^{2}-5^{2}$$

The square of \sqrt{7} is 7.

$$4\times 7-5^{2}$$

Multiply 4 and 7 to get 28.

$$28-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$28-25$$

Subtract 25 from 28 to get 3.

$$3$$

Factor

$$3$$