Page 2 - LN-Multiplication in Algebra

Multiplying a Monomial by a Polynomial

1. Multiplying a Monomial by a Binomial
To multiply a monomial with a binomial we have to multiply the monomial
with each term of the binomial.
Example

Multiplication of 8 and (x + y) will be (8x + 8y).

Multiplying a Polynomial by a Polynomial

1. Multiplying a Binomial by a Binomial

We use the distributive law of multiplication in this case. Multiply each term of a binomial
with every term of another binomial. After multiplying the polynomials we have to look
for the like terms and combine them.

Example
Simplify (3a + 4b) × (2a + 3b)

Solution:

(3a + 4b) × (2a + 3b)
= 3a × (2a + 3b) + 4b × (2a + 3b) [distributive law]

= (3a × 2a) + (3a × 3b) + (4b × 2a) + (4b × 3b)

2
= 6 a + 9ab + 8ba + 12b 2
2
= 6 a + 17ab + 12b 2 [Since ba = ab]

Multiplying a Binomial by a Trinomial

In this also we have to multiply each term of the binomial with every term of trinomial.

Example

2
Calculate the volume of a cuboidal box whose dimensions are 5x × 3x × 7x 4