Multiplication of Algebraic Expressions - Multiplying a Binomial by a Trinomial

Multiplying a Binomial by a Trinomial:

• In this multiplication, we shall have to multiply each of the three terms in the trinomial by each of the two terms in the binomial.

1) (a + 7) × (a² + 3a + 5) 
= a × (a² + 3a + 5) × 7 × (a² + 3a + 5) .... [using the distributive law]
= a³ + 3a² + 5a + 7a² + 21a + 35 
= a³ + (3a² + 7a²) + (5a + 21a) + 35
= a³ + 10a² + 26a + 35

2) Simplify (a + b)(2a – 3b + c) - (2a – 3b)c.

⇒ We have (a + b)(2a – 3b + c) = a (2a – 3b + c) + b (2a – 3b + c)

= 2a² – 3ab + ac + 2ab – 3b² + bc

= 2a² – ab – 3b² + bc + ac

and (2a – 3b)c = 2ac – 3bc

Therefore,

(a + b)(2a – 3b + c) – (2a – 3b)c

= 2a² – ab – 3b² + bc + ac – (2ac – 3bc)

= 2a² – ab – 3b² + bc + ac – 2ac + 3bc

= 2a² – ab – 3b² + (bc + 3bc) + (ac – 2ac)

= 2a² – 3b² – ab + 4bc – ac.