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

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

Evaluate

$$a^{2}-4b^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Cancel out 3 and 3.

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

Cancel out 3 and 3.

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

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

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

Divide -6 by 3 to get -2.

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

Combine 2ab and -2ba to get 0.

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

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

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

Multiply -6 and 2 to get -12.

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

Divide -12 by 3 to get -4.

$$a^{2}-4b^{2}$$

Expand

$$a^{2}-4b^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Cancel out 3 and 3.

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

Cancel out 3 and 3.

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

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

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

Divide -6 by 3 to get -2.

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

Combine 2ab and -2ba to get 0.

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

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

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

Multiply -6 and 2 to get -12.

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

Divide -12 by 3 to get -4.

$$a^{2}-4b^{2}$$