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Home >> Polynomials >> Multiplication of Polynomials >> Multiplication of Monomial & Binomial >>

Multiplication of Monomial & Binomial

Multiplication of Two or more Monomials Multiplication of Two or more Binomials Multiplication of Two or more Trinomials Multiplication of Monomial & Binomial Multiplication of Monomial & Trinomial
Multiplication of Binomial & Trinomial

Before you understand this concept, you are advised to read:

What are Monomials & Binomials ?
What are Terms of Polynomial ?

While multiplying a monomial and a binomial you will find following situations:

  • Multiply Monomial and Binomial
    Example 1: Multiply 2a and (3a - 4)
    Example 2: Multiply 4x and (x + y)

  • Multiply Binomial and Monomial
    Example 3: Multiply (4 + q) and q2
    Example 4: Multiply (a - b) and c


    Multiply Monomial and Binomial:

    Example 1: Multiply 2a and (3a - 4)
    Solution: As per given question:

    Monomial = 2a
    Binomial = (3a - 4)

    Write in the multiplication expression and we get:
    2a (3a - 4)

    Use Distributive Law and multiply monomial with every term of binomial & this is done in the following steps:
    = (2a X 3a) - (2a X 4)
    = 6a2 - 8a

    Hence, 2a (3a - 4) = 6a2 - 8a

    Example 2: Multiply 4x and (x + y)
    Solution: As per given question:

    Monomial = 4x
    Binomial = (x + y)

    Write in the multiplication expression and we get:
    4x (x + y)

    Use Distributive Law and multiply monomial with every term of binomial & this is done in the following steps:
    = (4x X x) + (4x X y)
    = 4x2 + 4xy

    Hence, 4x (x + y) = 4x2 + 4xy


    Multiply Binomial and Monomial

    Example 3: Multiply (4 + q) and q2
    Solution: As per given question:

    Binomial = 4 + q
    Monomial = q2

    Write in the multiplication expression and we get:
    (4 + q) q2

    Use Distributive Law and multiply monomial with every term of binomial & this is done in the following steps:
    = (4 X q2)+ (q X q2)
    = 4q2 + q3

    Or we can write it as:
    = q3 + 4q2

    Hence, (4 + q) q2 = q3 + 4q2

    Example 4: Multiply (a - b) and c
    Solution: As per given question:

    Binomial = (a - b)
    Monomial = c

    Write in the multiplication expression and we get:
    (a - b) c

    Use Distributive Law and multiply monomial with every term of binomial & this is done in the following steps:
    = (a X c) - (b X c)
    = ac - bc

    Hence, (a - b) c = ac - bc
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