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Multiplication of a Monomial by a Trinomial

While multiplying a monomial by a trinomial, we follow the same procedure as that of multiplying
a monomial by a binomial, i.e., each term of the trinomial is multiplied by the monomial using
the distributive property.
2
Example 10: Multiply (–6x) by (2x – 13x – 5)
Solution: Horizontal method Column method

2x – 13x – 5
2
2
(–6x) × (2x – 13x – 5)
2
= (–6x × 2x ) – (–6x × 13x) – (–6x × 5) 3 × (–6x)
2
3
2
= –12x + 78x + 30x –12x + 78x + 30x
Multiplication of a Binomial by another Binomial
While multiplying a binomial, say (a + b) with another binomial, say (c + d) we follow these steps:

Step 1: Write the product of two binomials i.e., (a + b) × (c + d).
Step 2: Use of Distributive Law: Multiply the first term of the first binomial by the second binomial
and then multiply the second term of the first binomial by the second binomial, i.e., a × (c + d) +
b × (c + d).
Step 3: Simplify and then add like terms, i.e., ac + ad + bc + bd.
2
2
Example 11: Multiply (p – 2) by (p + s ) by using horizontal and column method.
Solution: Horizontal method: We have,
2
2
2
3
2
(p – 2) × (p + s ) = p × (p + s ) + (–2) × (p + s ) = p + ps – 2p – 2s 2
2
2
2
2
Column method: We have, p – 2
× p + s 2
2
3
2
2
p – 2p [Multiplying (p – 2) by p ]
2
2
2
+ s p – 2s [Multiplying (p – 2) by s ]
2
2
3
p – 2p + s p – 2s 2 [Add the terms vertically]
Quick Check
Kiara has a rectangular park in front of her house, which has a length (x + 5y) units and a breadth (3x – 2y)
units. Find the area of the rectangular park. Also evaluate the value of the area if x = 2.5 and y = 3.
Multiplication of a Binomial by a Trinomial
While multiplying a binomial by a trinomial, we follow the same procedure as that of multiplying
a binomial by another binomial, i.e., each of the three terms of the trinomial is multiplied by each
of the two terms of the binomial.
2
Example 12: Multiply (4x – 2x + 5) by (2x + 3) by horizontal and column method.
Solution: Horizontal method

2
2
2
We have, (4x – 2x + 5) × (2x + 3) = (4x – 2x + 5) × (2x) + (4x – 2x + 5) × (3) [Using distributive law]
3
2
2
= 8x – 4x + 10x + 12x – 6x + 15
2
3
= 8x + 8x + 4x + 15 [Adding like terms]
201 Algebraic Expressions