Algebra is often regarded by many primary and secondary school students as a challenging topic to learn in mathematics. In these examples, we’ll do the 4 parts of Patterns and Algebra by using simple exam questions as illustrations. (More on **expanding double brackets worksheet** **and other maths worksheets**, check out the links at the end of this resource page)

‘Simplify’ is commonly used in many exam questions. However, it may require you to find the value of an ‘unknown’ by applying one of the fours below:

**1. Factorising **

**2. Expanding**

**3. Substituting**

**4. Solving**

Perhaps, it is important to note that learning how to factorise, expand, substitute and solve algebra early in Grade 7 and 8 is crucial.

## 1. Factorising

Factorise the following expressions (note that expanding and factorising are opposites)

**a.** 2a + 10 =

Highest Common Factor (HCF) of 2a and 10 is 2

2(a + 10)

**b.** 4 + 6x =

HCF = 2

2(2 + 3x)

**c.** 3x – 9=

3 (x – 3)

**d.** 2x^2 + 4x

HCF = 2x

2x (x + 2)

## 2. Substitution

**a.** Write down the value of *abc* when *a*=10,* b*=2 and* c*=0

*abc = 10x2x0=0*

*Common wrong answer 20*

*Maths knowledge: any number x 0 is 0*

**b. **Work out the value of 1/2*x* – 3*y* when *x*= 10 and *y*= 2

5 – 6 = – 1 (many students write 1 instead)

Concept tested: Addition and subtraction of -ve and +ve numbers. (Reinforce that differences that 6-5=1and 5-6=-1)

c. Find the value of 3x + 2y when x = 4 and y = 5

12 – 10 = 2 …………. 🙂

## 3. Expanding single and double brackets

(Note that expanding and factorising are opposites)

Expand the following expressions

a. 3(2y – 5) =

6y – 15 ( many student forget to do 3 x – 15)

b. 4(2m + 3n) =

8m + 12n

c. x(x – 10) =

x^2 – 10x

## 4. Solving equation

Solve the following equations to find the value of x

a. 4x = 20

x = 5

b. 1) 3x – 7 = 8

2) 3x = 8 + 7 ( it is important to get the order 8 + 7 right and not 7 + 8: even the answer is same, the answer is NOT be the same when subtracting, see the example below)

3) 3x = 15

4) x = 5

c. 8(x + 12) = 100

8x + 96 = 100 ………………Expand the brackets

8x = 100 – 96………………. (subtract 96 on both sides (remember balancing equations?)

x = 4/8 (Why divide by 8? In order to find the value of x, you must divide LHS and RHS by 8)

x = 1/2 (or 0.5)

Solve the following to find the value of y

a. y/3 = 9

y = 27 ………….multiply 3 x 9 (now, this is important as you can use this to solve complex equations that have a divisor)

b. 2y/5 = 4

2y = 20………. ( 20 = 5 x 4)

y = 10

c. 2y + 3 / 2 = 5

2y + 3 = 10………. ( 10 = 2 x 5)

2y = 10 – 3 ………..(subtracting 3 on both sides of the equation)

2y = 7

y = 7/2

y = 3.5

## General Algebra Techniques

The 4 techniques for solving algebra problems are discussed above: Factorising, Expanding, Substituting and Solving. You can use this to address expanding double brackets and other extension ideas in Algebra.

We have a lot of free resources and explanations like this to help you. Check out all the **other worksheets** including the expanding double brackets free worksheets PDF on this page.

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