Algebra Basics (Edexcel IGCSE Maths)

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Author

Paul

Last updated

17 March 2023

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Substitution

What is substitution?

Substitution is where we replace letters in a formula with their values
This allows you to find one other value that is in the formula

How do we substitute numbers into a formula?

Write down the formula, if not clearly stated in question
Substitute the numbers given, using brackets around negative numbers, (-3), (-5) etc
Simplify any calculations if you can
Rearrange the formula if necessary (it is usually easier to substitute first)
Work out the calculation

Worked example

(a)

Find the value of the expression

2 x (x + 3 y)

when

x = 2

and

y = - 4

Substitute the numbers given.
Use brackets () around negative numbers that you have substituted so that you don't forget about them.
It is a good idea to show every step of working to make sure that you are following the order of operations correctly.

$\begin{array}{rcl} 2 \times 2 \times (2 + 3 \times (- 4)) \\ = & 2 \times 2 \times (2 - 12) \\ = & 2 \times 2 \times (- 10) \\ = & 4 \times - 10 \end{array}$

$- 40$

(b)

The formula

P = 2 l + 2 w

is used to find the perimeter, P, of a rectangle of length

l

and width

w

Given that the rectangle has a perimeter of 20 cm and a width of 4 cm, find its length.

Substitute the values you are given into the formula.

$20 = 2 \times l + 2 \times 4$

Simplify.

$20 = 2 l + 8$

Subtract 8 from both sides.

$12 = 2 l$

Divide both sides by 2.

$l = 6 cm$

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Collecting Like Terms

How do we collect like terms?

TERMS are separated by + or –
- The sign belongs to the coefficient of the term after the symbol
- If there is no symbol in front of the first term then this is a positive term
  - 2x - 3y means +2 x's and -3 y's
“LIKE” terms must have exactly the same LETTERS AND POWERS (the COEFFICIENT can be different)
- Examples of like terms:
  - 2x and 3x
  - 2x² and 3x²
  - 2xy and 3xy
  - 4(x + y) and 5(x + y)
- Examples that are NOT like terms
  - 2x and 3y (different letters)
  - 2x² and 3x⁴(different powers)
  - 2xy and 3xyz (different letters)
  - 4(x + y) and 5(x + y)² (different powers)
- Remember multiplication can be done in any order
  - xy and yx are like terms
Add the COEFFICIENTS of like terms
- If the answer is a positive answer then put "+" in front if there are other terms before it
  - x - 2y + 5y = x + 3y
- If the answer is a negative number then put "-" in front
  - x - 5y + 2y = x - 3y

Examiner Tip

A “coefficient” answers the question “how many?”

For example:

the coefficient of x in 2x² – 5x + 2 is -5

and:

the coefficient of x in ax² + bx + c is b

Worked example

Simplify $x^{2} - 3 x y + 2 x^{2} + 4 x - 2 x y - x + 7$ .

Reorder the terms so that the $x^{2}$ 's are together, as are the $x y$ 's, $x$ 's and the constants.
Make sure that you keep the same sign in front of them when you reorder them.

$x^{2} + 2 x^{2} - 3 x y - 2 x y + 4 x - x + 7$

Add the coefficients of the 'like' terms.

$3 x^{2} - 5 x y + 3 x + 7$

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