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

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

Evaluate

$$6x^{2}+\frac{7x}{3}+\frac{2}{9}$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+\frac{1}{3} by each term of 3x+\frac{2}{3}.

$$6x^{2}+2x\times \frac{2}{3}+\frac{1}{3}\times 3x+\frac{1}{3}\times \frac{2}{3}$$

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

$$6x^{2}+\frac{2\times 2}{3}x+\frac{1}{3}\times 3x+\frac{1}{3}\times \frac{2}{3}$$

Multiply 2 and 2 to get 4.

$$6x^{2}+\frac{4}{3}x+\frac{1}{3}\times 3x+\frac{1}{3}\times \frac{2}{3}$$

Cancel out 3 and 3.

$$6x^{2}+\frac{4}{3}x+x+\frac{1}{3}\times \frac{2}{3}$$

Combine \frac{4}{3}x and x to get \frac{7}{3}x.

$$6x^{2}+\frac{7}{3}x+\frac{1}{3}\times \frac{2}{3}$$

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$6x^{2}+\frac{7}{3}x+\frac{1\times 2}{3\times 3}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$6x^{2}+\frac{7}{3}x+\frac{2}{9}$$

Expand

$$6x^{2}+\frac{7x}{3}+\frac{2}{9}$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+\frac{1}{3} by each term of 3x+\frac{2}{3}.

$$6x^{2}+2x\times \frac{2}{3}+\frac{1}{3}\times 3x+\frac{1}{3}\times \frac{2}{3}$$

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

$$6x^{2}+\frac{2\times 2}{3}x+\frac{1}{3}\times 3x+\frac{1}{3}\times \frac{2}{3}$$

Multiply 2 and 2 to get 4.

$$6x^{2}+\frac{4}{3}x+\frac{1}{3}\times 3x+\frac{1}{3}\times \frac{2}{3}$$

Cancel out 3 and 3.

$$6x^{2}+\frac{4}{3}x+x+\frac{1}{3}\times \frac{2}{3}$$

Combine \frac{4}{3}x and x to get \frac{7}{3}x.

$$6x^{2}+\frac{7}{3}x+\frac{1}{3}\times \frac{2}{3}$$

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$6x^{2}+\frac{7}{3}x+\frac{1\times 2}{3\times 3}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$6x^{2}+\frac{7}{3}x+\frac{2}{9}$$