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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply \frac{2}{3} by a+3b.

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

Cancel out 3 and 3.

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

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

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

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

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

Express \frac{2}{3}\left(-3\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

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

Divide -6 by 3 to get -2.

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

Expand

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

Solution Steps

Use the distributive property to multiply \frac{2}{3} by a+3b.

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

Cancel out 3 and 3.

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

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

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

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

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

Express \frac{2}{3}\left(-3\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

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

Divide -6 by 3 to get -2.

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