What We Have Discussed?

There are number of situations in which we need to multiply algebraic expressions.

A monomial multiplied by a monomial always gives a .

While multiplying a polynomial by a monomial, we multiply term in the polynomial by the monomial.

In carrying out the multiplication of an algebraic expression with another algebraic expression (monomial/binomial/trinomial etc.) we multiply term by term i.e. every term of the expression is multiplied by every term in the another expression.

An identity is an equation, which is for all values of the variables in the equation. On the other hand, an equation is true only for certain values of its variables. An equation is notis an identity.

The following are identities:

I. a+b2 = a2 + 2ab + b2

II. a−b2 = a2 - 2ab + b2

III. (a + b) (a - b) = a2 - b2

IV. (x + a) (x + b) = x2 + (a + b) x + ab

The above four identities are useful in carrying out squares and products of algebraic expressions. They also allow easy alternative methods to calculate products of numbers.