Multiplying Binomials Answers

Introduction to multiplying binomials answers:

In mathematics, binomials are one of the interesting topics in polynomials. Binomials are defined as the process of sum or difference of more than one monomial or it can be defined as two monomials. Multiplying is one of the basic arithmetic operations. Let us solve some example problems for multiplying binomials with answers.

Example for Binomials:

(x + 2)

Multiplying Binomials Answers - Different Methods:

Different methods for multiplying binomials are,

Distributive method
Vertical method
Grid method
Foil Method

Distributive method:

It is the defined as multiplying each term in the first binomial is multiplied with the each term in the second binomials.

Vertical method:

The process of multiplying the given binomials in vertical and combine the like terms are called as vertical method.

Grid method:

The process of multiplying the given binomial values in the table form is called as grid method. In the grid, row or column can be replaced by each term. Multiply the rows and columns in the grid and the result of the like terms can be combined together.

Foil method:

FOIL is defined as First Outer Inner Last

It performs the multiplication operation in the way of first term, outer term, inner term and then last term in the each parentheses.

Multiplying Binomials Answers - Example Problems:

Some example problems for multiplying binomials are,

Example 1:

Determine the answers for the given binomials using distributive method for multiplying binomials

(3x + 7) (4x - 12)

Solution:

Given

(3x + 7) (4x - 12)

Distributive method

First term 3x in the first binomial can be multiplied with the second binomial terms

3x . (4x - 12)

12x2 – 36x

Second term 7 in the first binomial can be multiplied with the second binomial terms

7 (4x - 12)

28x - 84

Combine the like terms

12x2 - 36x + 28x  - 84

12x2 - 8x - 84

Answer:

12x2 - 8x - 84

Example 2:

Determine the answer for the given binomials using vertical method for multiplying binomials

(7x – 6) (x – 14)

Solution:

Given

(7x – 6) (x – 14)

7x – 6

x – 14           

7x2 – 6x                  multiplying the first binomial 7x – 6 from the second binomial term x

- 98x + 84            multiplying first binomials 7x – 6 from the second binomial term – 14

7x2 – 114x + 84            combine the like terms then we get result

Answer:

7x2 – 1140x + 84

Algebra is widely used in day to day activities watch out for my forthcoming posts on Multiplying Polynomials by Monomials and Multiply Trinomials. I am sure they will be helpful.

Example 3:

Determine the answer for the given binomials using grid method for multiplying binomials

(8x + 3) (2x + 5)

Solution:

Given

(8x + 3) (2x + 5)

Combine the like terms

6x + 15 + 16x2 + 40x

16x2 + 46x + 15

Answer:

16x2 + 46x + 15

Example 4:

Determine the answer for the given binomials using Foil method for multiplying binomials

(3x + 5) (8x + 12)

Solution:

Given

(3x + 5) (8x + 12)

Multiply the First term in the given binomials

3x (8x)

24x2

Multiply the outer terms in the given binomials

3x (12)

36x

Multiply the inner terms in the given binomials

5 (8x)

40x

Multiply the last term in the binomial

5 (12)

60

Add the like terms

24x2 + 36x + 40x + 60

24x2 + 76x + 60

Answer:

24x2 + 76x + 60