Solve (3a+b/2)(4a-b/3)

$$( 3 a + \frac { b } { 2 } ) ( 4 a - \frac { b } { 3 } )$$

Evaluate

$$\frac{\left(12a-b\right)\left(6a+b\right)}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3a times \frac{2}{2}.

$$\left(\frac{2\times 3a}{2}+\frac{b}{2}\right)\left(4a-\frac{b}{3}\right)$$

Since \frac{2\times 3a}{2} and \frac{b}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\times 3a+b}{2}\left(4a-\frac{b}{3}\right)$$

Do the multiplications in 2\times 3a+b.

$$\frac{6a+b}{2}\left(4a-\frac{b}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4a times \frac{3}{3}.

$$\frac{6a+b}{2}\left(\frac{3\times 4a}{3}-\frac{b}{3}\right)$$

Since \frac{3\times 4a}{3} and \frac{b}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6a+b}{2}\times \frac{3\times 4a-b}{3}$$

Do the multiplications in 3\times 4a-b.

$$\frac{6a+b}{2}\times \frac{12a-b}{3}$$

Multiply \frac{6a+b}{2} times \frac{12a-b}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(6a+b\right)\left(12a-b\right)}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\left(6a+b\right)\left(12a-b\right)}{6}$$

Apply the distributive property by multiplying each term of 6a+b by each term of 12a-b.

$$\frac{72a^{2}-6ab+12ba-b^{2}}{6}$$

Combine -6ab and 12ba to get 6ab.

$$\frac{72a^{2}+6ab-b^{2}}{6}$$

Expand

$$ab-\frac{b^{2}}{6}+12a^{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3a times \frac{2}{2}.

$$\left(\frac{2\times 3a}{2}+\frac{b}{2}\right)\left(4a-\frac{b}{3}\right)$$

Since \frac{2\times 3a}{2} and \frac{b}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\times 3a+b}{2}\left(4a-\frac{b}{3}\right)$$

Do the multiplications in 2\times 3a+b.

$$\frac{6a+b}{2}\left(4a-\frac{b}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4a times \frac{3}{3}.

$$\frac{6a+b}{2}\left(\frac{3\times 4a}{3}-\frac{b}{3}\right)$$

Since \frac{3\times 4a}{3} and \frac{b}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6a+b}{2}\times \frac{3\times 4a-b}{3}$$

Do the multiplications in 3\times 4a-b.

$$\frac{6a+b}{2}\times \frac{12a-b}{3}$$

Multiply \frac{6a+b}{2} times \frac{12a-b}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(6a+b\right)\left(12a-b\right)}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{\left(6a+b\right)\left(12a-b\right)}{6}$$

Apply the distributive property by multiplying each term of 6a+b by each term of 12a-b.

$$\frac{72a^{2}-6ab+12ba-b^{2}}{6}$$

Combine -6ab and 12ba to get 6ab.

$$\frac{72a^{2}+6ab-b^{2}}{6}$$