Solve (frac{-7+sqrt{97}}{2}+3)(frac{-7+sqrt{97}}{2}+4)

$$( \frac{ -7+ \sqrt{ 97 } }{ 2 } +3)( \frac{ -7+ \sqrt{ 97 } }{ 2 } +4)$$

Evaluate

$$24$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\left(\frac{-7+\sqrt{97}}{2}+\frac{3\times 2}{2}\right)\left(\frac{-7+\sqrt{97}}{2}+4\right)$$

Since \frac{-7+\sqrt{97}}{2} and \frac{3\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-7+\sqrt{97}+3\times 2}{2}\left(\frac{-7+\sqrt{97}}{2}+4\right)$$

Do the multiplications in -7+\sqrt{97}+3\times 2.

$$\frac{-7+\sqrt{97}+6}{2}\left(\frac{-7+\sqrt{97}}{2}+4\right)$$

Do the calculations in -7+\sqrt{97}+6.

$$\frac{-1+\sqrt{97}}{2}\left(\frac{-7+\sqrt{97}}{2}+4\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{2}{2}.

$$\frac{-1+\sqrt{97}}{2}\left(\frac{-7+\sqrt{97}}{2}+\frac{4\times 2}{2}\right)$$

Since \frac{-7+\sqrt{97}}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-1+\sqrt{97}}{2}\times \frac{-7+\sqrt{97}+4\times 2}{2}$$

Do the multiplications in -7+\sqrt{97}+4\times 2.

$$\frac{-1+\sqrt{97}}{2}\times \frac{-7+\sqrt{97}+8}{2}$$

Do the calculations in -7+\sqrt{97}+8.

$$\frac{-1+\sqrt{97}}{2}\times \frac{1+\sqrt{97}}{2}$$

Multiply \frac{-1+\sqrt{97}}{2} times \frac{1+\sqrt{97}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-1+\sqrt{97}\right)\left(1+\sqrt{97}\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(-1+\sqrt{97}\right)\left(1+\sqrt{97}\right)}{4}$$

Apply the distributive property by multiplying each term of -1+\sqrt{97} by each term of 1+\sqrt{97}.

$$\frac{-1-\sqrt{97}+\sqrt{97}+\left(\sqrt{97}\right)^{2}}{4}$$

Combine -\sqrt{97} and \sqrt{97} to get 0.

$$\frac{-1+\left(\sqrt{97}\right)^{2}}{4}$$

The square of \sqrt{97} is 97.

$$\frac{-1+97}{4}$$

Add -1 and 97 to get 96.

$$\frac{96}{4}$$

Divide 96 by 4 to get 24.

$$24$$

Factor

$$2^{3}\times 3$$