- Algebraic Expression
- Terms are formed by the product of variables and constants, e.g. –3xy, 2xyz, 5×2, etc.
- Terms are added to form expressions, e.g. –2xy + 5×2.
- Expressions that contain exactly one, two and three terms are called monomials, binomials and trinomials, respectively.
- In general, any expression containing one or more terms with nonzero coefficients (and with variables having non-negative exponents) is called a polynomial.
- Like terms are formed from the same variables and the powers of these variables are also the same.
- But coefficients of like terms need not be the same.
- There are number of situations like finding the area of rectangle, triangle, etc. in which we need to multiply algebraic expressions.
- Multiplication of two algebraic expressions is again an algebraic expression.
- A monomial multiplied by a monomial always gives a monomial.
- While multiplying a polynomial by a monomial, we multiply every term in the polynomial by the monomial using the distributive law a ( b + c) = ab + ac.
- In the multiplication of a polynomial by a binomial (or trinomial), we multiply term by term, i.e. every term of the polynomial is multiplied by every term in the binomial (or trinomial) using the distributive property.
- An identity is an equality, which is true for all values of its variables in the equality, i.e. an identity is a universal truth.
- An equation is true only for certain values of its variables.
- Some standard identities: (i) (a + b) 2 = a2 + 2ab + b2 (ii) (a – b) 2 = a2 – 2ab + b2 (iii) (a + b) (a – b) = a2 – b2 (iv) (x + a) (x + b) = x2 + (a + b) x + ab

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