Expressions, formulae and Equations 2

Expressions, formulae and Equations 2

By Maman Firmansyah

Learning Objectives

After learning this material, students will be able to:​

expand brackets.

use the HCF to factorise an expression.

Subject | Maths

Learning Objectives

Multiple Choice

Double a number then add 5.

• 2n + 5

• 2(n + 5)

• 2n - 5

• 2n : 5

Multiple Choice

The sum of a number and 14

• n + 14

• n - 14

• 14 - n

• 14n

Multiple Choice

Add 5 to a number then double it

• 2(n + 5)

• (n + 5)/2

• n + 5(2)

• 2(n - 5)

Multiple Choice

The formula of Force is:

$$F=m\cdot a$$  , where F is Force, m is mass and a is acceleration.

What is the value of F, when m = 0.5 kg and a = 20 m/s²

• 10 kg.m/s²

• 100 kg.m/s²

• 1 kg.m/s²

• 40 kg.m/s²

2.3 Expanding brackets

Subject | Maths

Expanding brackets

​To expand brackets, multiply each term inside the brackets by the term directly in front of the brackets.

Example 1​

Subject | Maths

Expanding brackets

​Expand the bracket: 3(2a - b)

​

Answer:

​

3(2a - b) = 3 x 2a + 3 x (-b)​

3(2a - b)​ = 6a - 3b

Example 2​

Subject | Maths

Expanding brackets

​Expand the bracket: a(2a - 3b + 4c)

​

Answer:

​

a(2a - 3b + 4c) = a x 2a + a x (-3b)​ + a x 4c

a(2a - 3b + 4c)​ = 2a² - 3ab + 4ac

Example 3​

Subject | Maths

Expanding brackets

​Expand and simplify this expression: 4(2x + 3x²) − x(6 + x)

​

Answer:

​

4(2x + 3x²) − x(6 + x) = 4.2x + 4.3x² - x.6 - x.x

4(2x + 3x²) − x(6 + x) = 8x + 12x² - 6x - x²

4(2x + 3x²) − x(6 + x) =​ 2x + 11x²

Multiple Choice

Expand the brackets:

10(f + 5)

• 10f + 50
• f + 50 
• 10f + 5 
• b + c 

Multiple Choice

Which of the following is the correct expansion of:
5(r - 2)?

• 5r - 2
• 5r +2
• 5r + 10
• 5r - 10

Multiple Choice

Which of the following is the correct expansion of:
3p(4p - 7q)?

• 7p - 10pq
• 12pq - 21q²
• 9q
• 12p² - 21pq

2.4 Factorising

Subject | Maths

Factorising

​To expand a term with brackets, you multiply each term inside the brackets by the term outside the brackets.

​

​

​​

When you factorise an expression, you take the highest common factor (HCF) and put it outside the brackets.​

​

​

Example 4​

Subject | Maths

Factoring

​Factorise the expression: 2x - 10

​

Answer:

​

​2x - 10 = 2(x - 5) ---------------> HCF of 2 and 10 is 2. So, 2 is put outside the brackets

Example 5​

Subject | Maths

Factorising

​Factorise the expression: 4a + 8ab

​

Answer:

​

​4a + 8ab = 4a(1 + 2b) ---------------> HCF of 4a and 8ab is 4a. So, 4a is put outside the brackets