Multiplication of two Binomials

Multiplication of two binomials can be solved in both horizontal and column method.

Horizontal method:

Follow the following steps to multiply the binomials in the horizontal method:

1. First write the two binomials in a row separated by using multiplication sign.

2. Multiply each term of one binomial with each term of the other.

3. In the product obtained, combine the like terms and then add the like terms.

Therefore, we will learn how to multiply two binomials a + 5 by a + 7 using horizontal method.

a + 5 by a + 7

= (a + 5) ∙ (a + 7), [separate the two binomials using multiplication sign]

= a ∙ (a + 7) + 5 ∙ (a + 7), [multiplying each term of the first binomial with each term of the second binomial]

= a ∙ a + a ∙ 7 + 5 ∙ a + 5 ∙ 7

= a² + 7a + 5a + 35, [combine the like terms]

= a² + 12a + 35

Column method:

Follow the following steps to multiply the binomials in the column method:

1. Write the two binomials in two rows one below the other.

2. Multiply one term of the binomial in lower line (i.e. second row) with each term of the binomial in the upper line (i.e. first row) and write the product in the third row.

3. Multiply second term of the binomial in lower line (i.e. second row) with each term of the binomial in upper line (i.e. first row) and write the product in the fourth row in such a way that the like terms are one below the other.

4. Add the like terms column wise.

Therefore, we will learn how to multiply two binomials 5a - 6b and 7a + 8b using column method.

Solved examples on multiplication of two binomials:

1. Multiply 3x² – 6y² by 2x² + 4y²

Solution:

3x² – 6y² by 2x² + 4y²

= (3x² – 6y²) ∙ (2x² + 4y²), [separate the two binomials using multiplication sign]

= 3x² ∙ (2x² + 4y²) – 6y² ∙ (2x² + 4y²), [multiplying each term of the first binomial with each term of the second binomial]

= 6x⁴ + 12x²y² – 12x²y² – 24y⁴

= 6x⁴ + 12x²y² – 12x²y² – 24⁴, [combine the like terms]

= 6x⁴ - 24⁴

2. Multiply (m + 6) by (3m – 2)

Solution:

The above examples will help us to solve the multiplication of two binomials in horizontal method and in column method.

● Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials

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