Page 142 - ICSE Math 6

Example 3: Multiply.
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(a) –6 and –3x (b) 13 and 2ab (c) 30a and 4a b (d) 2ab and xyz
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Solution: (a) (–6) × (–3x ) = {(–6) × (–3)} × x = 18x 2
(b) 13 × 2ab = (13 × 2) × ab = 26ab
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(c) 30a × 4a b = (30 × 4) × (a × a b) = 120a b
(d) 2ab × xyz = 2 × (ab × xyz) = 2abxyz
Use of Brackets as Grouping Symbols
While performing fundamental operations on algebraic expressions, we use brackets to group terms.
Also, while simplifying an expression, first of all, terms inside a bracket are operated. There are four
types of brackets:

(a) Small bracket or parentheses denoted by ( ).
(b) Middle bracket or curly bracket denoted by { }.
(c) Big bracket or square bracket denoted by [ ]. ____

(d) Bar bracket or vinculum denoted by a horizontal line drawn over terms.
When removing brackets from an algebraic expression, first of all the bar bracket is removed, then
the small bracket followed by the curly bracket, and finally the square bracket is removed.

Removing a bracket

When there is a positive (+) sign before a bracket Maths Info
Bracket is removed and the sign of all the terms inside the bracket If there is a constant or a variable
are retained as it is. For example, written outside a bracket, then
while removing the bracket
(a) x + (2y – z) = x + 2y – z each term of the expression

(b) 2a + (10 – q) = 2a + 10 – q inside the bracket is multiplied
by that constant or variable.
When there is a negative (–) sign before a bracket
Bracket is removed and the sign of all the terms inside the bracket are changed. For example,
(a) p – (q – r) = p – q + r

(b) 20 – (–11 + a) = 20 + 11 – a
Example 4: Simplify.

(a) 3a + (b – 5a) (b) 10 – 2{3b – 4a(10 – 5)}
(c) x – 2 −   {–5y + ( 2 –10 8x− )}  

Solution: (a) 3a + (b – 5a) = 3a + b – 5a (Removing small bracket)

= b – 2a
(b) 10 – 2{3b – 4a(10 – 5)} = 10 – 2{3b – 4a(5)} ( Simplifying terms in
small bracket)
= 10 – 2{3b – 20a} (Removing small bracket)
= 10 – {6b – 40a}
= 10 – 6b + 40a (Removing curly bracket)

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