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Home >> Polynomials >> Multiplication of Polynomials >> Multiplication of Monomial & Trinomial >> Multiplication of Monomial & 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 trinomial you will find following situations:
Multiply Monomial and Trinomial
Example 1: Multiply 5a and (a + b + c)
Example 2: Multiply 3p and (p2 + p - 2)
Multiply Trinomial and Monomial
Example 3: Multiply (4q2 - 2q + 8) and 2q
Example 4: Multiply (a + b - c) and z
Multiply Monomial and Trinomial
Example 1: Multiply 5a and (a + b + c)
Solution: As per given question:
Monomial = 5a
Trinomial = (a + b + c)
Write in the multiplication expression and we get:
5a (a + b + c)
Use Distributive Law and multiply monomial with every term of trinomial & this is done in the following steps:
= (5a X a) +(5a X b) + (5a X c)
= 5a2 + 5ab + 5ac
Hence, 5a (a + b + c) = 5a2 + 5ab + 5ac
Example 2: Multiply 3p and (p2 + p - 2)
Solution: As per given question:
Monomial = 3p
Trinomial = (p2 + p - 2)
Write in the multiplication expression and we get:
3p (p2 + p - 2)
Use Distributive Law and multiply monomial with every term of trinomial & this is done in the following steps:
= (3p X p2) + (3p X p) - (3p X 2)
= 3p3 + 3p2 - 6p
Hence, 3p (p2 + p - 2) = 3p3 + 3p2 - 6p
Multiply Trinomial and Monomial
Example 3: Multiply (4q2 - 2q + 8) and 2q
Solution: As per given question:
Trinomial = (4q2 - 2q + 8)
Monomial = 2q
Write in the multiplication expression and we get:
(4q2 - 2q + 8) 2q
Use Distributive Law and multiply monomial with every term of trinomial & this is done in the following steps:
= (4q2 X 2q) - (2q X 2q) + (8 X 2q)
= 8q3 - 4q2 + 16q
Hence, (4q2 - 2q + 8) 2q = 8q3 - 4q2 + 16q
Example 4: Multiply (a + b - c) and z
Solution: As per given question:
Trinomial = (a + b - c)
Monomial = z
Write in the multiplication expression and we get:
(a + b - c) z
Use Distributive Law and multiply monomial with every term of trinomial & this is done in the following steps:
= (a X z) + (b X z) - (c X z)
= az + bz - cz
Hence, (a + b - c) z = az + bz - cz
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