Solve 2/5[5(x-2)(x-4)+5]

$$\frac { 2 } { 5 } [ 5 ( x - 2 ) ( x - 4 ) + 5 ]$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 5 by x-2.

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

Apply the distributive property by multiplying each term of 5x-10 by each term of x-4.

$$\frac{2}{5}\left(5x^{2}-20x-10x+40+5\right)$$

Combine -20x and -10x to get -30x.

$$\frac{2}{5}\left(5x^{2}-30x+40+5\right)$$

Add 40 and 5 to get 45.

$$\frac{2}{5}\left(5x^{2}-30x+45\right)$$

Use the distributive property to multiply \frac{2}{5} by 5x^{2}-30x+45.

$$\frac{2}{5}\times 5x^{2}+\frac{2}{5}\left(-30\right)x+\frac{2}{5}\times 45$$

Cancel out 5 and 5.

$$2x^{2}+\frac{2}{5}\left(-30\right)x+\frac{2}{5}\times 45$$

Express \frac{2}{5}\left(-30\right) as a single fraction.

$$2x^{2}+\frac{2\left(-30\right)}{5}x+\frac{2}{5}\times 45$$

Multiply 2 and -30 to get -60.

$$2x^{2}+\frac{-60}{5}x+\frac{2}{5}\times 45$$

Divide -60 by 5 to get -12.

$$2x^{2}-12x+\frac{2}{5}\times 45$$

Express \frac{2}{5}\times 45 as a single fraction.

$$2x^{2}-12x+\frac{2\times 45}{5}$$

Multiply 2 and 45 to get 90.

$$2x^{2}-12x+\frac{90}{5}$$

Divide 90 by 5 to get 18.

$$2x^{2}-12x+18$$

Expand

$$2x^{2}-12x+18$$

Solution Steps

Use the distributive property to multiply 5 by x-2.

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

Apply the distributive property by multiplying each term of 5x-10 by each term of x-4.

$$\frac{2}{5}\left(5x^{2}-20x-10x+40+5\right)$$

Combine -20x and -10x to get -30x.

$$\frac{2}{5}\left(5x^{2}-30x+40+5\right)$$

Add 40 and 5 to get 45.

$$\frac{2}{5}\left(5x^{2}-30x+45\right)$$

Use the distributive property to multiply \frac{2}{5} by 5x^{2}-30x+45.

$$\frac{2}{5}\times 5x^{2}+\frac{2}{5}\left(-30\right)x+\frac{2}{5}\times 45$$

Cancel out 5 and 5.

$$2x^{2}+\frac{2}{5}\left(-30\right)x+\frac{2}{5}\times 45$$

Express \frac{2}{5}\left(-30\right) as a single fraction.

$$2x^{2}+\frac{2\left(-30\right)}{5}x+\frac{2}{5}\times 45$$

Multiply 2 and -30 to get -60.

$$2x^{2}+\frac{-60}{5}x+\frac{2}{5}\times 45$$

Divide -60 by 5 to get -12.

$$2x^{2}-12x+\frac{2}{5}\times 45$$

Express \frac{2}{5}\times 45 as a single fraction.

$$2x^{2}-12x+\frac{2\times 45}{5}$$

Multiply 2 and 45 to get 90.

$$2x^{2}-12x+\frac{90}{5}$$

Divide 90 by 5 to get 18.

$$2x^{2}-12x+18$$