Solve 1/2left(2x+5right)left(3x+6right)

$$\frac{ 1 }{ 2 } \left( 2x+5 \right) \left( 3x+6 \right)$$

Evaluate

$$\frac{3\left(x+2\right)\left(2x+5\right)}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x+5.

$$\left(\frac{1}{2}\times 2x+\frac{1}{2}\times 5\right)\left(3x+6\right)$$

Cancel out 2 and 2.

$$\left(x+\frac{1}{2}\times 5\right)\left(3x+6\right)$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$\left(x+\frac{5}{2}\right)\left(3x+6\right)$$

Apply the distributive property by multiplying each term of x+\frac{5}{2} by each term of 3x+6.

$$3x^{2}+6x+\frac{5}{2}\times 3x+\frac{5}{2}\times 6$$

Express \frac{5}{2}\times 3 as a single fraction.

$$3x^{2}+6x+\frac{5\times 3}{2}x+\frac{5}{2}\times 6$$

Multiply 5 and 3 to get 15.

$$3x^{2}+6x+\frac{15}{2}x+\frac{5}{2}\times 6$$

Combine 6x and \frac{15}{2}x to get \frac{27}{2}x.

$$3x^{2}+\frac{27}{2}x+\frac{5}{2}\times 6$$

Express \frac{5}{2}\times 6 as a single fraction.

$$3x^{2}+\frac{27}{2}x+\frac{5\times 6}{2}$$

Multiply 5 and 6 to get 30.

$$3x^{2}+\frac{27}{2}x+\frac{30}{2}$$

Divide 30 by 2 to get 15.

$$3x^{2}+\frac{27}{2}x+15$$

Expand

$$3x^{2}+\frac{27x}{2}+15$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x+5.

$$\left(\frac{1}{2}\times 2x+\frac{1}{2}\times 5\right)\left(3x+6\right)$$

Cancel out 2 and 2.

$$\left(x+\frac{1}{2}\times 5\right)\left(3x+6\right)$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$\left(x+\frac{5}{2}\right)\left(3x+6\right)$$

Apply the distributive property by multiplying each term of x+\frac{5}{2} by each term of 3x+6.

$$3x^{2}+6x+\frac{5}{2}\times 3x+\frac{5}{2}\times 6$$

Express \frac{5}{2}\times 3 as a single fraction.

$$3x^{2}+6x+\frac{5\times 3}{2}x+\frac{5}{2}\times 6$$

Multiply 5 and 3 to get 15.

$$3x^{2}+6x+\frac{15}{2}x+\frac{5}{2}\times 6$$

Combine 6x and \frac{15}{2}x to get \frac{27}{2}x.

$$3x^{2}+\frac{27}{2}x+\frac{5}{2}\times 6$$

Express \frac{5}{2}\times 6 as a single fraction.

$$3x^{2}+\frac{27}{2}x+\frac{5\times 6}{2}$$

Multiply 5 and 6 to get 30.

$$3x^{2}+\frac{27}{2}x+\frac{30}{2}$$

Divide 30 by 2 to get 15.

$$3x^{2}+\frac{27}{2}x+15$$