ABSTRACT
Only similar expressions can be added or subtracted as the addition and subtraction of dissimilar expressions will result in the wrong answer. In the expression 2a 3b a b, symbols a and b may be assumed to represent aerated concrete blocks and bricks respectively. As the two materials are different, the terms with ‘a’ (2a and a) need to be processed separately from the terms with ‘b’, i.e. 3b and b:
2a 3b a b 2a a 3b b 2a 1a 3b 1b (a 1a; b 1b) a 4b (simplify 2a 1a, separately
from 3b 1b)
EXAMPLE 3.1
Simplify:
(a) 5a 2b 3b 2a
3.1 Introduction
3.2 Addition and subtraction
(a) Rearrange the terms of 5a 2b 3b 2a:
5a 2b 3b 2a 5a 2a 3b 2b
7a b (5a 2a 7a; 3b 2b 1b or b)
(b) Rearrange the terms of 5x 3y 2x 3y:
5x 3y 2x 3y 2x 5x 3y 3y
3x 6y (2x 5x 3x; 3y 3y 6y)
Multiplication of letters is done in the same manner as the multiplication of numbers. For example:
5 5 52
a a a2 (also see the chapter on indices)
As in addition and subtraction, only the similar terms are multiplied. Although in addition and subtraction y2 and y3 are treated as different terms, but in multiplication and division they can be multiplied and/or divided as the base, in this case ‘y’, is the same. Examples 3.2 and 3.3 explain the processes of multiplication and division involving simple algebraic expressions. For complex questions (for example, multiply 5a2 2a 6 by 2a2 8a 3) refer to a textbook on analytical methods.
