Page 164 - Maths Class 06

EXAMPLE 1. The side of a regular octagon is denoted by l. Express the perimeter of the octagon in terms
of l. l l

SOLUTION : The side of regular octagon = l l l

Perimeter of the regular octagon = ´8 Side l l

= 8l l l
EXAMPLE 2. A cube is a three-dimensional figure as shown in the figure. It has six faces and all of them
are identical squares. The length of an edge of the cube is given by l. Find the formula for
the total length of the edges of a cube.

SOLUTION : The length of an edge of the cube = l
l
Number of edges in a cube = 12
l
Therefore, the total length of the edges of the given cube = 12l. l

EXAMPLE 3. Make three expressions with numbers 3, 4 and 7 (not variables) using operations of
addition, subtraction or multiplication. All numbers should be used, but not more than
once.

SOLUTION : (a) (3 + ) 4 - 7 (b) 3 ´( 4 + 7) (c) (4 + ) 7 + 3
EXAMPLE 4. Which out of the following are expressions with numbers only?
(a) x + 4 (b) 7y -( 8 3´ ) (c) 5 21 7( - ) + 7 2´ + x
(d) 8 (e) 4 + 3n (d) (3 51´ ) (2+ ´ - ) 3
SOLUTION : The expressions with numbers only are (d) and (f).

Types of Algebraic Expressions
Monomials
NOTE
An expression which contains only one term is known
as a monomial. xy is a monomial, but x + y is a
binomial.
2
For example : 2x, 3xy , – 5abc, – 9, etc. are monomials.
2xy is a monomial, but 2 + x + y
Binomials is a trinomial.
An expression containing two terms is called a binomial.
2
For example : 6 – y, 2x + 3y x, 2 – 5xy z, etc. all are binomials.
Trinomials
An expression containing three terms is called a trinomial. NOTE
3
3
3
2
For example : 2 + x – y, a + b + c, x – y + z , 6 + xyz + x ,
The symbol or number appearing before a
etc. all are trinomials. variable used in an algebraic term is called
Quadrinomials its coefficient.
For example, in –3xy, –3x is the coefficient
An expression containing four terms is called a quadrinomial.
y and –3y is the coefficient of x, etc.
2
2
2
3
3
3
For example : x + y + z – xyz, x + y + z – 3 xyz,
etc. all are quadrinomial.
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