Multiplying Binomials is the process of multiplying one binomial with another. Bi means 2 so you multiply two terms together. say for example multiplying (a + b)(a – b), Here (a + b) is one term and ( a – b) is another term. The product of these two algebraic terms gives the final result.
1. The FOIL method:
This stands for “First, Outside, Inside, Last.” This method involves multiplying the first term of one binomial by the first term of the other, the first term of one binomial by the second term of the other, the second term of one binomial by the first term of the other, and the second term of one binomial by the second term of the other. The results are then added together to give the final answer.
In general, this is of the form (a + b)(c + d) = ac + ad + bc + bd. A special mnemonic has been developed to describe this result: FOIL, or First + Outer + Inner + Last which terms are defined below:
• First: Multiply the first terms of both binomials―ac
• Outer: Multiply the outer terms of both binomials, the first term of the first binomial and the last term of the last binomial―ad
• Inner: Multiply the inner term of both binomials, the last term of the first binomial and the first term of the last binomial―bc
• Last: Multiply the last term of both binomials―bd
2.The distributive property:
This method involves distributing one term of one binomial to both terms of the other binomial, then adding the two products together.
The distributive property is used to derive the product of a monomial and binomials or trinomials. The distributive property is also used to derive the product of a binomial and another binomial or polynomial. Let’s consider the example of the product of two binomials as follows:
(15x + 8)(22x + 4)
Applying this general distributive property to the example product of two binomials above, we have,
15x(22x) + 15x(4) + 8(22x) + 8 (4)
where we have made the following substitutions: a = 15x, b = 8, c = 22x, and d = 4. Next we perform the multiplications to obtain,
330x^2 + 60x + 176x + 32
Finally, we simplify by combining like terms (the 60x and the 176x), to obtain the final result,
330x^2 + 236x + 32
Let’s do one more example together, this time using some negative terms:
(-11x + 6)(5x – 18)
Using the distributive property (FOIL method), we have,
-11x(5x) + 11x(18) + 6(5x) – 6(18)
3. BOX Method:
Step 1: Make a box where each cell row and column is a term. Using the example (x+7)(3x + 5)
| x | 7 | |
| 3x | ||
| 5 |
Step 2: Do the multiplication
| x | 7 | |
| 3x | 3x2 | 21x |
| 5 | 5x | 21 |
Step 3: Add all the terms
3x2 + 21x + 5x + 21 = 3×2 + 26x + 21
Conclusion:
There are 3 main methods explained above. Apart from this while solving sometimes you need to use various formulas like (a+b)(a+b), (a-b)(a-b), (a+b)(a-b)
FAQ:
What is binomial?
Bi means two so binomial means two algebraic terms
What are 3 methods for multiplying binomials?
FOIL, Distributive and BOX are three main methods for multiplying binomials
How do you multiply binomials fast?
BOX method is the fastest method to do multiplication
What are two ways to multiply binomials to binomials?
FOIL, Distributive and BOX are three main methods for multiplying binomials
What is the best method in multiplying binomials?
It depends on which method you are comfortable with. Using any method will lead to the same solution.
How to Multiply Binomials and Trinomials?
FOIL, Distributive, and BOX all these methods can be applied to multiply binomials and trinomials
Multiplying Binomials Worksheet with answers
This article provides free worksheet below that can be downloaded
What is an example of a binomials?
(3x + 5)(2x-7) is one the example of binomial
How do you solve a binomial with exponents?
The above example shows how to multiply binomial with exponent
How do you multiply polynomials with exponents?
Multiply each term with another and once done multiply with the next term.
How do you multiply expressions with exponents?
To multiply expressions with exponents, first identify the base and exponent of each expression. Then multiply the bases together and add the exponents together to get your answer. For example, to multiply 8^3 * 7^2, you would take 8*7 = 56 and 3+2 = 5; so the answer is 56^5.
Can you multiply variables with exponents?
Yes the multiplication of variables with exponents is possible
How do you foil 4 terms?
To foil 4 terms, you would multiply the first term in each set of parentheses and then add that product to the product of the second term in each set of parentheses. Keep continuing the process till you reach final result where no terms can be added
How do you expand brackets to the power of 4?
Using binomial theorem helps to expand brackets to the power of 4
Multiplying Binomials Notes pdf
Binomials Notes provided below
Multiplying Binomials Quiz
Below is a quiz that will help you to check your knowledge of this topic
