How to Multiply Binomials & Combine Like Terms

Multiplying Two Binomials

• 1

  Examine the expression (3a + 16)^2. This expression reads "the quantity of three a plus 16 squared." Raised power, or squared, indicates that the binomial in the parenthesis will be multiplied by itself.

• 2

  Rewrite the problem using parenthetical notation, (3a + 16)(3a + 16).

• 3

  Multiply the binomials with the distributive property. Multiply the first terms together, 3a x 3a = 9a^2. Multiply the outside terms, 3a x 16 = 48a. Multiply the inside terms, 16 x 3a = 48a. Multiply the last terms, 16 x 16 = 256. The multiplied expression now reads 9a^2 + 48a + 48a + 256.

• 4

  Combine like terms. This means to add together the terms that have the same variable. Because no other term in this polynomial has the variable "a" raised to a power, the term 9a^2 is left as it is. In addition, the number 256 is called a constant since it has no variable and cannot change. Because there are no more constants within the polynomial, it is left as it is also. However, two terms do have the same variable and those are 48a and 48a.

• 5

  Add 48a + 48a, which equals 96a.

• 6

  Rewrite the expression in its simplest form, 9a^2 + 96a + 256.

Multiplying Three Binomials

• 7

  Examine the expression (a + b)^3. Write the expression out in parenthetic notation, (a + b)(a + b)(a + b).

• 8

  Multiply the first two binomials using the distributive property. Multiply the first terms, a x a = a^2. Multiply the outside terms, a x b = ab. Multiply the inside terms, a x b = ab. Finally, multiply the last terms, b x b = b^2. The expression reads a^2 + ab + ab + b^2.

• 9

  Combine like terms, ab + ab = 2ab, simplifying the expression to a^2 + 2ab + b^2.

• 10

  Multiply the simplified expression by the third binomial, (a^2 + 2ab + b^2)(a + b). Multiply each term in the simplified expression by each term in the binomial.

  a^2 x a = a^3

  a^2 x b = a^2b (Remember that the exponent stays only on the variable it originally belonged to. The solution to a^2 x b is very different from ab^2.)

  2ab x a = 2a^2b

  2ab x b = 2b^2a

  b^2 x a = b^2a

  b^2 x b = b^3.

• 11

  Simplify the solution: a^3 + a^2b + 2a^2b + 2b^2a + b^2a + b^3.

• 12

  Combine like terms, a^3 + 3a^2b + 3b^2a + b^3.