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

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

Evaluate

$$\left(2x+5\right)\left(3x+1\right)$$

Solution Steps

Use the distributive property to multiply 6 by x+\frac{1}{3}.

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

Multiply 6 and \frac{1}{3} to get \frac{6}{3}.

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

Divide 6 by 3 to get 2.

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

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

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

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

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

Multiply 6 and 5 to get 30.

$$6x^{2}+\frac{30}{2}x+2x+2\times \frac{5}{2}$$

Divide 30 by 2 to get 15.

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

Combine 15x and 2x to get 17x.

$$6x^{2}+17x+2\times \frac{5}{2}$$

Cancel out 2 and 2.

$$6x^{2}+17x+5$$

Expand

$$6x^{2}+17x+5$$

Solution Steps

Use the distributive property to multiply 6 by x+\frac{1}{3}.

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

Multiply 6 and \frac{1}{3} to get \frac{6}{3}.

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

Divide 6 by 3 to get 2.

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

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

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

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

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

Multiply 6 and 5 to get 30.

$$6x^{2}+\frac{30}{2}x+2x+2\times \frac{5}{2}$$

Divide 30 by 2 to get 15.

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

Combine 15x and 2x to get 17x.

$$6x^{2}+17x+2\times \frac{5}{2}$$

Cancel out 2 and 2.

$$6x^{2}+17x+5$$