Choose two binomials to multiply. For example, suppose your given (3a + 4b)(7a + 3b).
Multiply the first terms of the two binomials. So multiply 3a by 7a to get 21a^2.
Multiply the outside terms in the binomials. These would be the first term of the first binomial and the second term of the second binomial. In the example, you would multiply 3a by 3b to obtain 9ab.
Multiply the inside terms -- that is, the second term in the first binomial and the first term in the second binomial. In the example, you would multiply 4b by 7a, yielding 28ab.
Try to combine the outside and inside products. In the example, 9ab + 28ab = 37ab. Use this combined term in your final answer.
Multiply the last terms of the binomials. In the example, calculate 4b * 3b. The product would be 12b^2.
Combine all your calculations to get the final result. So (3a + 4b)(7a + 3b) is equal to 21(a^2) + 37ab + 12(b^2).