If you are wondering how to do the Multiplication of Two Binomials together? Don’t Worry anymore as we have included different methods like horizontal, vertical, and FOIL Methods of Binomial Multiplication in this article along with examples.
Multiplying Binomials with small tricks will helps you to solve all the binomial multiplication problems easily. To know all the tricks to do multiplication of two binomials, check out this 6th Grade Math Binomial Multiplication concept.
Also, check
- Multiplication of Two Monomials
- Multiplication of Polynomial by Monomial
- Worksheet on Dividing Monomials
What does Multiplying Binomials Mean?
Multiplication of two Binomials is also similar to Multiplying whole numbers or fractions. The binomial is an expression that consists of two terms that are connected by a plus or minus sign.
How do you Multiply Binomials? | Product of Two Binomials
There are various methods included to multiply binomials. Multiply the terms of one binomial with other terms of binomial and then finally take the algebraic sum of these products. Let us check the different methods that are used to multiply binomials.
Multiplying Binomials using Distributive Property | Horizontal Method of Binomial Multiplication
Multiplying Binomials using Distributive Property is also known as Multiplying Binomials using Horizontal method. Follow the below procedure to find the Multiplication of two Binomials.
- First, take the two binomials and write one binomial after another binomial in a row separated by using the multiplication sign.
- Multiply each term of the first binomial with each term of the other binomial.
- Then, apply the Distributive Property and expand each term individually.
- In the resultant obtained, combine the like terms and then add the like terms.
Example: Multiply m + 2 by m + 3
Solution: Given binomials are m + 2 and m + 3.
The first binomial is m + 2 and the second binomial is m + 3.
Separate the two binomials using the multiplication sign.
(m + 2) × (m + 3)
Multiply each term of the first binomial with each term of the second binomial.
m ∙ (m + 3) + 2 ∙ (m + 3)
Now, apply the distributive property i.e, a . (b + c) = (a . b) + (a . c)
(m × m) + (m × 3) + (2 × m) + (2 × 3) = m2 + 3m + 2m + 6
Now, combine the like terms.
m2 + 5m + 6
Therefore, the multiplication of two binomials is m2 + 5m + 6.
Multiplying Two Binomials using FOIL Method
The method of multiplying two binomials using the FOIL Method is explained here. If you are searching for what does FOIL stands for in multiplying binomial here is the answer. The FOIL denotes F – First, O – Outer, I – Inner, L – Last. The FOIL formula is: (a + b)(c + d) = ac + ad + bc + bd. The below process will explain to you how to multiply two binomials using the FOIL Method.
- F – First: take the two binomials and multiply the first terms of both the binomials.
- O – Outer: The first term of the first binomial and second term of the second binomial is known as outer terms. Multiply the outer terms of both the binomials.
- I – Inner: Then, consider the second term of the first binomial and the first term of the second binomial and multiply them.
- Finally, Multiply the second term of both the binomials which are also known as the last terms of the binomials.
- In the resultant obtained, combine the like terms and then add the like terms.
Example:
Multiply y + 5 and y + 2 using the FOIL Method
Solution:
Given binomials are y + 5 and y + 2.
The first binomial is y + 5 and the second binomial is y + 2.
Multiply the first terms of both the binomials.
y × y = y2
Multiply the outer terms of both the binomials.
y × 2 = 2y
Multiply the inner terms of both the binomials.
5 × y = 5y
Multiply the last terms of both the binomials.
5 × 2 = 10.
Now, combine the like terms.
y2 + 2y + 5y + 10 = y2 + 7y + 10
Therefore, the multiplication of two binomials is y2 + 7y + 10.
Multiplication of Two Binomials using Vertical Method | Column Method of Binomial Multiplication
The vertical method of multiplying Two Binomials is also called the Column method of Two Binomial Multiplication. This Verticle Method of two binomial multiplication applies to all polynomial multiplications. The below process will help you to learn the Multiplication of Two Binomials using Vertical Method.
- First, take the two binomials and write one binomial below another binomial in two rows separated by using the multiplication sign.
- Multiply one term of the binomial in the second row (i.e. lower line) with each term of the binomial in the first row (i.e. upper line) and write the product in the third row.
- Multiply the second term of the binomial in the second row (i.e. lower line) with each term of the binomial in the first row (i.e. upper line) and write the product in the fourth row. Make sure to write the fourth row in such a way that all the like terms are one below the other.
- Add the like terms column-wise.
Example:
Multiply 4a – 5b and 6a + 7b using column method.
Solution:
Given binomials are 4a – 5b and 6a + 7b.
Write one binomial below another binomial in two rows separately.
4a – 5b
× 6a + 7b
—————
24a2 – 30ab (Multiplying 4a – 5b by 6a)
+ 28ab – 35b2Â (Multiplying 4a – 5b by 7b)
————————————
24a2 – 2ab – 35b2
Therefore, the answer is 24a2 – 2ab – 35b2
Multiplying Two Binomials Examples
Question 1.
Multiply 6a2 – 12b2 by 4a2 + 8b2
Solution:
Given binomials are 6a2 – 12b2 by 4a2 + 8b2
The first binomial is 4a2 + 8b2 and the second binomial is 6a2 – 12b2.
Separate the two binomials using the multiplication sign.
(4a2 + 8b2) × (6a2 – 12b2)
Multiply each term of the first binomial with each term of the second binomial.
4a2 ∙ (6a2 – 12b2) + 8b2 ∙ (6a2 – 12b2)
Now, apply the distributive property i.e, a . (b + c) = (a . b) + (a . c)
(4a2 × 6a2) – (4a2 × 12b2) + (8b2 × 6a2) – (8b2 × 12b2) = 24a4 – 48a2b2 + 48a2b2 – 96b4.
Now, combine the like terms.
24a4 – 96b4.
Therefore, the multiplication of two binomials is 24a4 – 96b4.
Question 2.
Multiply (3a + 4) by (2a – 6)
Solution:
Given binomials are (3a + 4) and (2a – 6).
The first binomial is 2a – 6 and the second binomial is 3a + 4.
Multiply the first terms of both the binomials.
2a × 3a = 6a2
Multiply the outer terms of both the binomials.
2a × 4 = 8a
Multiply the inner terms of both the binomials.
-6 × 3a = -18a
Multiply the last terms of both the binomials.
-6 × 4 = -24.
Now, combine the like terms.
6a2Â + 8a – 18a – 24 = 6a2 – 10a – 24
Therefore, the multiplication of two binomials is 6a2 – 10a – 24.
Question 3.
Find the product of 2m3 + 4n2 by m2 + 3n2
Solution:
Given binomials are 2m3 + 4n2 and m2 + 3n2.
Write one binomial below another binomial in two rows separately.
m2 + 3n2
× 2m3 + 4n2
—————
2m5 + 6m3n2 (Multiplying m2 + 3n2 by 2m3)
+ 8m2n2 + 12n4Â (Multiplying m2 + 3n2 by 4n2)
————————————
2m5 + 6m3n2 + 8m2n2 + 12n4Â
Therefore, the answer is 2m5 + 6m3n2 + 8m2n2 + 12n4Â .
Question 4.
Multiply 12p + 3 by 3p + 4
Solution:
Given binomials are 3p + 4 and 12p + 3.
The first binomial is 3p + 4 and the second binomial is 12p + 3.
Separate the two binomials using the multiplication sign.
(3p + 4) × (12p + 3)
Multiply each term of the first binomial with each term of the second binomial.
3p ∙ (12p + 3) + 4 ∙ (12p + 3)
Now, apply the distributive property i.e, a . (b + c) = (a . b) + (a . c)
(3p × 12p) + (3p × 3) + (4 × 12p) + (4 × 3) = 36p2 + 9p + 48p + 12
Now, combine the like terms.
36p2 + 57p + 12
Therefore, the multiplication of two binomials is 36p2 + 57p + 12.
FAQs on Multiplying Binomials
1. What is Multiplying Binomials?
It is an algebraic expression that consists of two terms attached with a plus or a minus sign is known as a binomial. Multiplying such binomials is known as the Multiplying Binomials.
2. What are the methods to multiply two binomials?
We have three different methods to do the Multiplication of Two Binomials. They are
- Horizontal Method
- Vertical Method
- FOIL Method
3. How to Multiply Binomials using Distributive Property?
Multiply Binomials using Distributive Property same as the multiplication of binomials using Horizontal method.
4. How to Multiply 3 Binomials?
First, we need to multiply two binomials. Then, the resultant need to multiply with the third binomial to get the product.
Conclusion
Read how to multiply binomials and solve all the problems given in this article. Effective learning will help you to grow towards success. Use our articles and practice well for the exam.