Solve ((x+9)+(x+3))*(x+2)+x(x+3)/2

$$( ( x + 9 ) + ( x + 3 ) ) \cdot ( x + 2 ) + \frac { x ( x + 3 ) } { 2 }$$

Evaluate

$$\frac{5x^{2}}{2}+\frac{35x}{2}+24$$

Short Solution Steps

Combine x and x to get 2x.

$$\left(2x+9+3\right)\left(x+2\right)+\frac{x\left(x+3\right)}{2}$$

Add 9 and 3 to get 12.

$$\left(2x+12\right)\left(x+2\right)+\frac{x\left(x+3\right)}{2}$$

Apply the distributive property by multiplying each term of 2x+12 by each term of x+2.

$$2x^{2}+4x+12x+24+\frac{x\left(x+3\right)}{2}$$

Combine 4x and 12x to get 16x.

$$2x^{2}+16x+24+\frac{x\left(x+3\right)}{2}$$

Use the distributive property to multiply x by x+3.

$$2x^{2}+16x+24+\frac{x^{2}+3x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2}+16x+24 times \frac{2}{2}.

$$\frac{2\left(2x^{2}+16x+24\right)}{2}+\frac{x^{2}+3x}{2}$$

Since \frac{2\left(2x^{2}+16x+24\right)}{2} and \frac{x^{2}+3x}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(2x^{2}+16x+24\right)+x^{2}+3x}{2}$$

Do the multiplications in 2\left(2x^{2}+16x+24\right)+x^{2}+3x.

$$\frac{4x^{2}+32x+48+x^{2}+3x}{2}$$

Combine like terms in 4x^{2}+32x+48+x^{2}+3x.

$$\frac{5x^{2}+35x+48}{2}$$

Expand

$$\frac{5x^{2}}{2}+\frac{35x}{2}+24$$

Short Solution Steps

Combine x and x to get 2x.

$$\left(2x+9+3\right)\left(x+2\right)+\frac{x\left(x+3\right)}{2}$$

Add 9 and 3 to get 12.

$$\left(2x+12\right)\left(x+2\right)+\frac{x\left(x+3\right)}{2}$$

Apply the distributive property by multiplying each term of 2x+12 by each term of x+2.

$$2x^{2}+4x+12x+24+\frac{x\left(x+3\right)}{2}$$

Combine 4x and 12x to get 16x.

$$2x^{2}+16x+24+\frac{x\left(x+3\right)}{2}$$

Use the distributive property to multiply x by x+3.

$$2x^{2}+16x+24+\frac{x^{2}+3x}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2}+16x+24 times \frac{2}{2}.

$$\frac{2\left(2x^{2}+16x+24\right)}{2}+\frac{x^{2}+3x}{2}$$

Since \frac{2\left(2x^{2}+16x+24\right)}{2} and \frac{x^{2}+3x}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(2x^{2}+16x+24\right)+x^{2}+3x}{2}$$

Do the multiplications in 2\left(2x^{2}+16x+24\right)+x^{2}+3x.

$$\frac{4x^{2}+32x+48+x^{2}+3x}{2}$$

Combine like terms in 4x^{2}+32x+48+x^{2}+3x.

$$\frac{5x^{2}+35x+48}{2}$$