Multiplication of Polynomial by Monomial
Multiplication of polynomial by monomial means every terms of the polynomial are multiplied by the monomial.
Multiplication of 3a2b – 5ab2 + 4ab and 2ab
First we will write the monomial (2ab) and the polynomial (3a2b – 5ab2 + 4ab) in the same row and then separate it by using the multiplication sign.
= 2ab × (3a2b – 5ab2 + 4ab)
Now we will multiply each term of the polynomial (3a2b – 5ab2 + 4ab) by the monomial (2ab)
= (2ab × 3a2b) – (2ab × 5ab2) + (2ab × 4ab)
= 6a3b2 – 10a2b3 + 8a2b2
Similarly, to find the product of 3x + 5y – 6z and - 5x
First we will write the monomial (5x) and the in the polynomial (3x + 5y – 6z) same row and then separate it by using the multiplication sign.
= -5x × (3x + 5y – 6z)
Now we will multiply each term of the polynomial (3x + 5y – 6z) by the monomial (-5x)
= (-5x × 3x) + (-5x × 5y) – (-5x × 6z)
= -15x2 – 25xy + 30xzSolved examples on multiplication of polynomial and monomial:
1. Find the product of x – y - z and -8x2.= -8x2 × (x – y – z)
= (-8x2 × x) – (-8x2 × y) – (-8x2 × z)
= -8x3 + 8x2y + 8x2z
2. Find the product of 5abc – 6a2bc – 6ab2c and 3abc2.
= 3abc2 × (5abc – 6a2bc – 6ab2c)
= (3abc2 × 5abc) – (3abc2 × 6a^2bc) – (3abc2 × 6ab2c)
= 15a2b2c3 - 18a3b2c3 - 18a2b3c3
3. Find the product of x2 + 2xy + y2 + 1 by z.
= z × (x2 + 2xy + y2 + 1)
= (z × x2) + (z × 2xy) + (z × y2) + (z × 1)
= x2z + 2xyz + y2z + z
4. Find the product of 4p3 – 12pq + 9q2 and -3pq.
= -3pq × (4p3 – 12pq + 9q2)
= (-3pq × 4p3) - (-3pq × 12pq) + (-3pq × 9q2)
= -12p4q + 36p2q2 – 27pq3
● Terms of an Algebraic Expression
Types of Algebraic Expressions
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
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