Solve 1/4*(5+4x)(8-x)

$$\frac { 1 } { 4 } \cdot ( 5 + 4 x ) ( 8 - x )$$

Evaluate

$$-x^{2}+\frac{27x}{4}+10$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 5+4x.

$$\left(\frac{1}{4}\times 5+\frac{1}{4}\times 4x\right)\left(8-x\right)$$

Multiply \frac{1}{4} and 5 to get \frac{5}{4}.

$$\left(\frac{5}{4}+\frac{1}{4}\times 4x\right)\left(8-x\right)$$

Cancel out 4 and 4.

$$\left(\frac{5}{4}+x\right)\left(8-x\right)$$

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

$$\frac{5}{4}\times 8+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

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

$$\frac{5\times 8}{4}+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

Multiply 5 and 8 to get 40.

$$\frac{40}{4}+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

Divide 40 by 4 to get 10.

$$10+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

Multiply \frac{5}{4} and -1 to get -\frac{5}{4}.

$$10-\frac{5}{4}x+8x-x^{2}$$

Combine -\frac{5}{4}x and 8x to get \frac{27}{4}x.

$$10+\frac{27}{4}x-x^{2}$$

Expand

$$-x^{2}+\frac{27x}{4}+10$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 5+4x.

$$\left(\frac{1}{4}\times 5+\frac{1}{4}\times 4x\right)\left(8-x\right)$$

Multiply \frac{1}{4} and 5 to get \frac{5}{4}.

$$\left(\frac{5}{4}+\frac{1}{4}\times 4x\right)\left(8-x\right)$$

Cancel out 4 and 4.

$$\left(\frac{5}{4}+x\right)\left(8-x\right)$$

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

$$\frac{5}{4}\times 8+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

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

$$\frac{5\times 8}{4}+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

Multiply 5 and 8 to get 40.

$$\frac{40}{4}+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

Divide 40 by 4 to get 10.

$$10+\frac{5}{4}\left(-1\right)x+8x-x^{2}$$

Multiply \frac{5}{4} and -1 to get -\frac{5}{4}.

$$10-\frac{5}{4}x+8x-x^{2}$$

Combine -\frac{5}{4}x and 8x to get \frac{27}{4}x.

$$10+\frac{27}{4}x-x^{2}$$