Expand (1/3a + b)(9b + 12): Binomial Multiplication with Fractions

The given expression is $(\frac{1}{3}a + b)(9b + 12)$. We will expand this expression using the distributive property:

Step 1: Multiply the first terms of each binomial:

• $\frac{1}{3}a \times 9b = 3ab$

Step 2: Multiply the outer terms:

• $\frac{1}{3}a \times 12 = 4a$

Step 3: Multiply the inner terms:

• $b \times 9b = 9b^2$

Step 4: Multiply the last terms:

• $b \times 12 = 12b$

Combine all the resulting terms together:

$9b^2 + 3ab + 4a + 12b$

Therefore, the solution to the problem is $9b^2 + 3ab + 4a + 12b$.