Algebraic Expressions: Understanding Monomials, Binomials, Trinomials, and Multiplication, Exercises of Mathematics

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ALGEBRAIC

EXPRESSIONS

WHAT IS ALGEBRAIC EXPRESSION?

 A number or a combination of numbers connected by the symbols of operation +,-,*,/ is called an algebraic expression. E.g.- 3x, 2x, -3/5 x. The no’s 3, 2, - 3, -3/5 used above are constants and the literal no’s x, y, z are variables. The several parts are called terms. The signs + and – connect the different terms. 2x and -3y are terms of the

WHAT ARE LIKE AND UNLIKE TERMS?

 Terms having same combinations of literal numbers are called like terms.  Terms do not having same combinations of literal numbers are called unlike terms. For e.g.-

1. 4ab, -3ba = Like terms
2. 3xy, -5ya = Unlike terms
3. 6 abc, -5acd = Unlike terms
4. 8pq, -3qp = Like terms

WHAT IS MULTIPLICATION OF

ALGEBRAIC EXPRESSIONS?

 The product of two numbers of like signs is positive and the product of two numbers of unlike signs is negative. For E.g., - 3 x 5 = 15; -4/5 x -5/ = 4/ -4 x 2 = -8; 3 x (-4/3) =

We also know the following laws of exponents  a x a = a  (a ) = a

WHAT IS MULTIPLICATION OF A

BINOMIAL BY A MONOMIAL?

 To multiply a binomial by a monomial, we use the following rule- a x (b + c) = a x b + a x c For E.g.- Multiply: 4b + 6 by 3a Product = 3a(4b + 6) = 3a x 4b + 3a x 6 = 12ab + 18a

WHAT IS MULTIPLICATION OF A

TRINOMIAL BY A MONOMIAL?

To multiply a trinomial by a monomial,

we use the following rule:

a x (b + c + d) = a x b + a x c + a x d

For e.g. –

Multiply: 3x – 2x + 2 by 3x

Product = 3x(3x – 2x + 2)

= 3x x 3x – 3x x 2x

+ 3x x 2

= 9x² - 6x² + 6x

WHICH ARE SPECIAL PRODUCTS

(IDENTITIES)?

The four special identities are:

1. (x + a) (x + b) = x + (a + b)x + ab For e.g. – (x + 3) (x + 2) = x + (3 + 2)x + 3 x 2 = x + 5x + 6
2. (a + b) = a + b + 2ab For e.g. – (3p + 4q) (3p + 4q) = (3p)² + (4q)² + 2 x 3p x 4q = 9p² + (16q)² +

3. (a – b) = a + b - 2ab For e.g.- (3p – 4q) (3p – 4q) = (3p)² + (4q)² -2 x 3p x 4q = (9p)² + (16q)² - 24pq.
4. (a - b ) = (a + b) (a – b) For e.g.- (a – b) - (a + b) = (a – b + a + b) (a – b – a – b) =2a x (-2b) =-4ab.

WHAT IS FACTORIZATION OF

ALGEBRAIC EXPRESSIONS?

The factors of-

 a+ 2ab + b are (a+b) (a+b)



 A -b are (a-b) (a +b)

 4x are-

1. 4 X x²
2. 2 X 2 X x²
3. 2 X 2 X x X x
4. 4 X x X x

 1 is a factor of every algebraic term, so 1 is called a trivial factor.

A – 2ab + b are (a-b) (a-b)

HOW DO WE DO FACTORIZATION BY

REGROUPING TERMS?

 Sometimes it is not possible to find the greatest common factor of the given set of monomials. But by regrouping the given terms, we can find the factors of the given expression. For e.g.,- 3xy + 2 + 6y + x = 3xy + 6y + x + 2 = 3y(x + 2)

• 1(x + 2) =(x + 2) (3y + 1)