# Substitution

Substitution means putting a number into a formula or expression in place of a letter

Example 1: Find the value of 4a + b when a = 5 and b = 3

In this question we are going to change a into 5 and b into 3

We cannot write 45 + 3 because 4b means 4 times b
We can instead use brackets to substitute the numbers into the expression:
4(5) + (3)

4(5) means 4 × 5
4 × 5 = 20

We now have: 20 + 3
20 + 3 = 23

Example 2: Find the value of 4a - 3b when a = 7 and b = 2

This time we are going to change a into 7 and b into 2

We can use brackets to substitute the numbers into the expression:
4(7) - 3(2)

4(7) means 4 × 7
4 × 7 = 28

3(2) means 3 × 2
3 × 2 = 6

We now have: 28 - 6
28 - 6 = 22

Example 3: Find the value of 4a2 - 3b when a = 3 and b = 7

4(3)2 - 3(7)

The order of operations tells us that the first step is to square the 3

32 = 9

We now have: 4(9) - 3(7)

4 × 9 = 36
3 × 7 = 21

36 - 21 = 15

Example 4: Find the value of 5a2 - ab when a = -3 and b = -2

5(-3)2 - (-3)(-2)

The order of operations tells us that the first step is to square the negative 3

A negative times a negative is a positive
(-3)2 = (-3) × (-3) = 9

We now have: 5(9) - (-3)(-2)

5 × 9 = 45
-3 × -2 = 6

45 - 6 = 39

Example 5: Find the value of 5ab - bc when a = 3, b = -2 and c = 4

5(3)(-2) - (-2)(4)

We can do the multiplication of 5 × 3 × -2 in any order
5 × 3 = 15
15 × -2 = -30 A positive times a negative is a negative

-2 × 4 = -8

We now have: -30 - -8

When we take away a negative we go up the number line -30 - - 8 = -30 + 8 = -22

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