Solve 2left(5n+1right)left(4n-4/5right)

$$2 \left( 5n+1 \right) \left( 4n- \frac{ 4 }{ 5 } \right)$$

Evaluate

$$40n^{2}-\frac{8}{5}$$

Solution Steps

Use the distributive property to multiply 2 by 5n+1.

$$\left(10n+2\right)\left(4n-\frac{4}{5}\right)$$

Apply the distributive property by multiplying each term of 10n+2 by each term of 4n-\frac{4}{5}.

$$40n^{2}+10n\left(-\frac{4}{5}\right)+8n+2\left(-\frac{4}{5}\right)$$

Express 10\left(-\frac{4}{5}\right) as a single fraction.

$$40n^{2}+\frac{10\left(-4\right)}{5}n+8n+2\left(-\frac{4}{5}\right)$$

Multiply 10 and -4 to get -40.

$$40n^{2}+\frac{-40}{5}n+8n+2\left(-\frac{4}{5}\right)$$

Divide -40 by 5 to get -8.

$$40n^{2}-8n+8n+2\left(-\frac{4}{5}\right)$$

Combine -8n and 8n to get 0.

$$40n^{2}+2\left(-\frac{4}{5}\right)$$

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

$$40n^{2}+\frac{2\left(-4\right)}{5}$$

Multiply 2 and -4 to get -8.

$$40n^{2}+\frac{-8}{5}$$

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

$$40n^{2}-\frac{8}{5}$$

Expand

$$40n^{2}-\frac{8}{5}$$

Solution Steps

Use the distributive property to multiply 2 by 5n+1.

$$\left(10n+2\right)\left(4n-\frac{4}{5}\right)$$

Apply the distributive property by multiplying each term of 10n+2 by each term of 4n-\frac{4}{5}.

$$40n^{2}+10n\left(-\frac{4}{5}\right)+8n+2\left(-\frac{4}{5}\right)$$

Express 10\left(-\frac{4}{5}\right) as a single fraction.

$$40n^{2}+\frac{10\left(-4\right)}{5}n+8n+2\left(-\frac{4}{5}\right)$$

Multiply 10 and -4 to get -40.

$$40n^{2}+\frac{-40}{5}n+8n+2\left(-\frac{4}{5}\right)$$

Divide -40 by 5 to get -8.

$$40n^{2}-8n+8n+2\left(-\frac{4}{5}\right)$$

Combine -8n and 8n to get 0.

$$40n^{2}+2\left(-\frac{4}{5}\right)$$

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

$$40n^{2}+\frac{2\left(-4\right)}{5}$$

Multiply 2 and -4 to get -8.

$$40n^{2}+\frac{-8}{5}$$

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

$$40n^{2}-\frac{8}{5}$$