Solve 3(a-2b)(1/3a+3/2b)

$$3 ( a - 2 b ) ( \frac { 1 } { 3 } a + \frac { 3 } { 2 } b )$$

Evaluate

$$\frac{\left(a-2b\right)\left(2a+9b\right)}{2}$$

Solution Steps

Use the distributive property to multiply 3 by a-2b.

$$\left(3a-6b\right)\left(\frac{1}{3}a+\frac{3}{2}b\right)$$

Apply the distributive property by multiplying each term of 3a-6b by each term of \frac{1}{3}a+\frac{3}{2}b.

$$3a\times \frac{1}{3}a+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b\times \frac{3}{2}b$$

Multiply a and a to get a^{2}.

$$3a^{2}\times \frac{1}{3}+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b\times \frac{3}{2}b$$

Multiply b and b to get b^{2}.

$$3a^{2}\times \frac{1}{3}+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

Cancel out 3 and 3.

$$a^{2}+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

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

$$a^{2}+\frac{3\times 3}{2}ab-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

Multiply 3 and 3 to get 9.

$$a^{2}+\frac{9}{2}ab-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

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

$$a^{2}+\frac{9}{2}ab+\frac{-6}{3}ba-6b^{2}\times \frac{3}{2}$$

Divide -6 by 3 to get -2.

$$a^{2}+\frac{9}{2}ab-2ba-6b^{2}\times \frac{3}{2}$$

Combine \frac{9}{2}ab and -2ba to get \frac{5}{2}ab.

$$a^{2}+\frac{5}{2}ab-6b^{2}\times \frac{3}{2}$$

Express -6\times \frac{3}{2} as a single fraction.

$$a^{2}+\frac{5}{2}ab+\frac{-6\times 3}{2}b^{2}$$

Multiply -6 and 3 to get -18.

$$a^{2}+\frac{5}{2}ab+\frac{-18}{2}b^{2}$$

Divide -18 by 2 to get -9.

$$a^{2}+\frac{5}{2}ab-9b^{2}$$

Expand

$$\frac{5ab}{2}+a^{2}-9b^{2}$$

Solution Steps

Use the distributive property to multiply 3 by a-2b.

$$\left(3a-6b\right)\left(\frac{1}{3}a+\frac{3}{2}b\right)$$

Apply the distributive property by multiplying each term of 3a-6b by each term of \frac{1}{3}a+\frac{3}{2}b.

$$3a\times \frac{1}{3}a+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b\times \frac{3}{2}b$$

Multiply a and a to get a^{2}.

$$3a^{2}\times \frac{1}{3}+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b\times \frac{3}{2}b$$

Multiply b and b to get b^{2}.

$$3a^{2}\times \frac{1}{3}+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

Cancel out 3 and 3.

$$a^{2}+3a\times \frac{3}{2}b-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

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

$$a^{2}+\frac{3\times 3}{2}ab-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

Multiply 3 and 3 to get 9.

$$a^{2}+\frac{9}{2}ab-6b\times \frac{1}{3}a-6b^{2}\times \frac{3}{2}$$

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

$$a^{2}+\frac{9}{2}ab+\frac{-6}{3}ba-6b^{2}\times \frac{3}{2}$$

Divide -6 by 3 to get -2.

$$a^{2}+\frac{9}{2}ab-2ba-6b^{2}\times \frac{3}{2}$$

Combine \frac{9}{2}ab and -2ba to get \frac{5}{2}ab.

$$a^{2}+\frac{5}{2}ab-6b^{2}\times \frac{3}{2}$$

Express -6\times \frac{3}{2} as a single fraction.

$$a^{2}+\frac{5}{2}ab+\frac{-6\times 3}{2}b^{2}$$

Multiply -6 and 3 to get -18.

$$a^{2}+\frac{5}{2}ab+\frac{-18}{2}b^{2}$$

Divide -18 by 2 to get -9.

$$a^{2}+\frac{5}{2}ab-9b^{2}$$