Solve 2/5(sqrt{13}-4)(sqrt{13}+4)

$$\frac { 2 } { 5 } ( \sqrt { 13 } - 4 ) ( \sqrt { 13 } + 4 )$$

Evaluate

$$-\frac{6}{5}=-1.2$$

Solution Steps

Use the distributive property to multiply \frac{2}{5} by \sqrt{13}-4.

$$\left(\frac{2}{5}\sqrt{13}+\frac{2}{5}\left(-4\right)\right)\left(\sqrt{13}+4\right)$$

Express \frac{2}{5}\left(-4\right) as a single fraction.

$$\left(\frac{2}{5}\sqrt{13}+\frac{2\left(-4\right)}{5}\right)\left(\sqrt{13}+4\right)$$

Multiply 2 and -4 to get -8.

$$\left(\frac{2}{5}\sqrt{13}+\frac{-8}{5}\right)\left(\sqrt{13}+4\right)$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\left(\frac{2}{5}\sqrt{13}-\frac{8}{5}\right)\left(\sqrt{13}+4\right)$$

Apply the distributive property by multiplying each term of \frac{2}{5}\sqrt{13}-\frac{8}{5} by each term of \sqrt{13}+4.

$$\frac{2}{5}\sqrt{13}\sqrt{13}+\frac{2}{5}\sqrt{13}\times 4-\frac{8}{5}\sqrt{13}-\frac{8}{5}\times 4$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$\frac{2}{5}\times 13+\frac{2}{5}\sqrt{13}\times 4-\frac{8}{5}\sqrt{13}-\frac{8}{5}\times 4$$

Express \frac{2}{5}\times 13 as a single fraction.

$$\frac{2\times 13}{5}+\frac{2}{5}\sqrt{13}\times 4-\frac{8}{5}\sqrt{13}-\frac{8}{5}\times 4$$

Multiply 2 and 13 to get 26.

$$\frac{26}{5}+\frac{2}{5}\sqrt{13}\times 4-\frac{8}{5}\sqrt{13}-\frac{8}{5}\times 4$$

Express \frac{2}{5}\times 4 as a single fraction.

$$\frac{26}{5}+\frac{2\times 4}{5}\sqrt{13}-\frac{8}{5}\sqrt{13}-\frac{8}{5}\times 4$$

Multiply 2 and 4 to get 8.

$$\frac{26}{5}+\frac{8}{5}\sqrt{13}-\frac{8}{5}\sqrt{13}-\frac{8}{5}\times 4$$

Combine \frac{8}{5}\sqrt{13} and -\frac{8}{5}\sqrt{13} to get 0.

$$\frac{26}{5}-\frac{8}{5}\times 4$$

Express -\frac{8}{5}\times 4 as a single fraction.

$$\frac{26}{5}+\frac{-8\times 4}{5}$$

Multiply -8 and 4 to get -32.

$$\frac{26}{5}+\frac{-32}{5}$$

Fraction \frac{-32}{5} can be rewritten as -\frac{32}{5} by extracting the negative sign.

$$\frac{26}{5}-\frac{32}{5}$$

Since \frac{26}{5} and \frac{32}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-32}{5}$$

Subtract 32 from 26 to get -6.

$$-\frac{6}{5}$$

Factor

$$-\frac{6}{5} = -1\frac{1}{5} = -1.2$$