Solve (1+1/4*x^2-1/2x+7/4)*(2+x)

$$(1+ \frac{ 1 }{ 4 } \times { x }^{ 2 } - \frac{ 1 }{ 2 } x+ \frac{ 7 }{ 4 } ) \times (2+x)$$

Evaluate

$$\frac{x^{3}+7x+22}{4}$$

Solution Steps

Add 1 and \frac{7}{4} to get \frac{11}{4}.

$$\left(\frac{11}{4}+\frac{1}{4}x^{2}-\frac{1}{2}x\right)\left(2+x\right)$$

Use the distributive property to multiply \frac{11}{4}+\frac{1}{4}x^{2}-\frac{1}{2}x by 2+x and combine like terms.

$$\frac{11}{2}+\frac{7}{4}x+\frac{1}{4}x^{3}$$

Expand

$$\frac{x^{3}}{4}+\frac{7x}{4}+\frac{11}{2}$$

Solution Steps

Add 1 and \frac{7}{4} to get \frac{11}{4}.

$$\left(\frac{11}{4}+\frac{1}{4}x^{2}-\frac{1}{2}x\right)\left(2+x\right)$$

Use the distributive property to multiply \frac{11}{4}+\frac{1}{4}x^{2}-\frac{1}{2}x by 2+x and combine like terms.

$$\frac{11}{2}+\frac{7}{4}x+\frac{1}{4}x^{3}$$