Solve {left(sqrt{9}3right)}^2-{left(3sqrt{2}-5sqrt{3}right)}^2=

$${ \left( \sqrt{ 9 } 3 \right) }^{ 2 } - { \left(3 \sqrt{ 2 } -5 \sqrt{ 3 } \right) }^{ 2 } =$$

Evaluate

$$30\sqrt{6}-12\approx 61.484692283$$

Solution Steps

Calculate the square root of 9 and get 3.

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

Multiply 3 and 3 to get 9.

$$9^{2}-\left(3\sqrt{2}-5\sqrt{3}\right)^{2}$$

Calculate 9 to the power of 2 and get 81.

$$81-\left(3\sqrt{2}-5\sqrt{3}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3\sqrt{2}-5\sqrt{3}\right)^{2}.

$$81-\left(9\left(\sqrt{2}\right)^{2}-30\sqrt{2}\sqrt{3}+25\left(\sqrt{3}\right)^{2}\right)$$

The square of \sqrt{2} is 2.

$$81-\left(9\times 2-30\sqrt{2}\sqrt{3}+25\left(\sqrt{3}\right)^{2}\right)$$

Multiply 9 and 2 to get 18.

$$81-\left(18-30\sqrt{2}\sqrt{3}+25\left(\sqrt{3}\right)^{2}\right)$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$81-\left(18-30\sqrt{6}+25\left(\sqrt{3}\right)^{2}\right)$$

The square of \sqrt{3} is 3.

$$81-\left(18-30\sqrt{6}+25\times 3\right)$$

Multiply 25 and 3 to get 75.

$$81-\left(18-30\sqrt{6}+75\right)$$

Add 18 and 75 to get 93.

$$81-\left(93-30\sqrt{6}\right)$$

To find the opposite of 93-30\sqrt{6}, find the opposite of each term.

$$81-93+30\sqrt{6}$$

Subtract 93 from 81 to get -12.

$$-12+30\sqrt{6}$$

Expand

$$30 \sqrt{6} - 12 = 61.484692283$$

Solution Steps

Calculate the square root of 9 and get 3.

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

Multiply 3 and 3 to get 9.

$$9^{2}-\left(3\sqrt{2}-5\sqrt{3}\right)^{2}$$

Calculate 9 to the power of 2 and get 81.

$$81-\left(3\sqrt{2}-5\sqrt{3}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3\sqrt{2}-5\sqrt{3}\right)^{2}.

$$81-\left(9\left(\sqrt{2}\right)^{2}-30\sqrt{2}\sqrt{3}+25\left(\sqrt{3}\right)^{2}\right)$$

The square of \sqrt{2} is 2.

$$81-\left(9\times 2-30\sqrt{2}\sqrt{3}+25\left(\sqrt{3}\right)^{2}\right)$$

Multiply 9 and 2 to get 18.

$$81-\left(18-30\sqrt{2}\sqrt{3}+25\left(\sqrt{3}\right)^{2}\right)$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$81-\left(18-30\sqrt{6}+25\left(\sqrt{3}\right)^{2}\right)$$

The square of \sqrt{3} is 3.

$$81-\left(18-30\sqrt{6}+25\times 3\right)$$

Multiply 25 and 3 to get 75.

$$81-\left(18-30\sqrt{6}+75\right)$$

Add 18 and 75 to get 93.

$$81-\left(93-30\sqrt{6}\right)$$

To find the opposite of 93-30\sqrt{6}, find the opposite of each term.

$$81-93+30\sqrt{6}$$

Subtract 93 from 81 to get -12.

$$-12+30\sqrt{6}$$