Expansion of Linear Expressions
Expansion usually involves removing the bracket.
=> a (b + c) = ab + ac
Expand 3( p + 2q)
3(p + 2q)
= 3 x p + 6 x q (Step : Use a ( b + c) = ab + ac)
= 3p + 6q
Example
(i) Expand 4 (a+ b)
= 4 x a + 4 x b (Step : Use a ( b + c) = ab + ac)
= 4a + 4b
(ii) Expand 4 + a
5
= 1 x (4 + a). (Step : Use a ( b + c) = ab + ac)
5
= 4 + 1a
5 5
= 4 + a
5 5
Examples
Expand and simplify
6(a + b) - 3a(2 - 5a)
= 6a + 6b - 6a +15a2 Step 1: Open/remove bracket
= 6a + 6b - 6a + 15a2 Step 2 : Group and simplify
= 15a2 +6b
Example
(1) Simplify (6y2– 4y – 3) – 2(2y2– 3y + 2)
(6y2– 4y – 3) – 2(2y2– 3y + 2) Step 1: Open bracket
= 6y2– 4y – 3 – 4y2+ 6y – 4 ( -2 x -3y = 6x [- x - = +] )
= 6y2– 4y2– 4y + 6y – 3 – 4 Step 2: Group variables (y2with y2, y, numbers)
= 2y2+ 2y – 7
(2) Simplify (2x2 + 2) + (3x2 + x + 1)
2x2 + 2 + 3x2 + x + 1 (Step 1 : Open bracket)
= 2x2 + 3x2 + x + 1 + 2 (Step2: Group x2, x , numbers)
= 5x2 + x + 3
(3) Simplify and factorise (2x2+ 3x - 7) + (3x2– 4x + 3)
2x2– 3x + 4 + 3x2– x - 3 (Step 1 : Open bracket)
= 2x2 + 3x2+ 3x – 4x - 7 + 3 (Step2: Group x2, x , numbers)
= 5x2– x - 4 (Step3 : Factorise)
= (5x - 4)(x - 1)
Expansion of 2 Linear Expressions
( a + b) ( c + d) = ac + ad + bc + bd
/\ /\
[ a x (c + d) + b x (c + d) ]
It is also called the "rainbow" arrow.
Practice
1. Expand the followings:
a. 5a(3 + b)
b. 2(9a - 2b)
c. 4(1 + 2a)
d. 7(3b - 4)
2. Expand the followings
a. (2a + b)(a + b)
b. (3a - b)(2a + b)
c. (4a - 2b)(a - b)
d. (2a + 7b)(2a - 3b
