Solve (4sqrt{3}+3sqrt{4})(4sqrt{3}-3sqrt{4})-4

$$(4 \sqrt{ 3 } +3 \sqrt{ 4 } )(4 \sqrt{ 3 } -3 \sqrt{ 4 } )-4$$

Evaluate

$$8$$

Solution Steps

Consider \left(4\sqrt{3}+3\sqrt{4}\right)\left(4\sqrt{3}-3\sqrt{4}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4\sqrt{3}\right)^{2}-\left(3\sqrt{4}\right)^{2}-4$$

Expand \left(4\sqrt{3}\right)^{2}.

$$4^{2}\left(\sqrt{3}\right)^{2}-\left(3\sqrt{4}\right)^{2}-4$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{3}\right)^{2}-\left(3\sqrt{4}\right)^{2}-4$$

The square of \sqrt{3} is 3.

$$16\times 3-\left(3\sqrt{4}\right)^{2}-4$$

Multiply 16 and 3 to get 48.

$$48-\left(3\sqrt{4}\right)^{2}-4$$

Calculate the square root of 4 and get 2.

$$48-\left(3\times 2\right)^{2}-4$$

Multiply 3 and 2 to get 6.

$$48-6^{2}-4$$

Calculate 6 to the power of 2 and get 36.

$$48-36-4$$

Subtract 36 from 48 to get 12.

$$12-4$$

Subtract 4 from 12 to get 8.

$$8$$

Factor

$$2^{3}$$