How do you substitute a number into an algebraic expression?

To substitute a number into an algebraic expression, all you need to do is re-write the expression in exactly the same way, except replacing the variable (letter) with the number. It always makes it clearer to put the number in brackets too. Then you can simplify your new expression and you have your answer!

Let's have a look at an example.

3x+7 where x = 5

So here, x is the variable and you are substituting in the number 5. All you do is write back the expression but with 5 instead of x. And don’t forget those brackets!

3(5) + 7

Now to simplify, just multiply out the brackets and add the 7:

3 x 5 + 7

= 15 + 7

= 22

And that’s your answer!

How about a harder example:

2y2 – 3y + 4 where y = 2

You do this one in exactly the same way, but this time the variable is y and the number is 2. So, write back the expression with 2 (in brackets!) instead of y:

2(2)2 – 3(2) + 4

And simplify… remember, always do the brackets first:

2 x 22 – 3 x 2 + 4

= 2 x 4 – 3 x 2 + 4

Multiplication always comes before addition and subtraction:

= 8 – 6 + 4

= 6

One more example, this time with two variables.

4x2 – y2 + 2xy where x = - 3 and y = 4

You have to be a bit more careful with this one – make sure you include the negative sign in the brackets when you replace x with (-3) and instead of y, write 4.

4(-3)2 – (4)2 + 2(-3)(4)

Start simplifying…

= 4 x (-3)2 – (4)2 + 2 x -3 x 4

Remember when you square a negative number you get a positive solution:

= 4 x 9 – 16 + 2 x -3 x 4

= 36 – 16 + (-24)

= - 4

Bethany H. A Level History tutor, GCSE Maths tutor, GCSE History tuto...

2 years ago

Answered by Bethany, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£18 /hr

Vlad B.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“Hi! I am studying Mathematics at Bath University and I am passionate about teaching, and learning mathematics.”

MyTutor guarantee

£18 /hr

Sophia H.

Degree: Biomedical Sciences (Bachelors) - Cardiff University

Subjects offered:Maths, Russian+ 1 more


“Hopeful doctor in the making looking to help you reach your goals! I'm interested in everything so I am sure we will have something in common. ”

£20 /hr

Ruchira R.

Degree: BA English (Bachelors) - Exeter University

Subjects offered:Maths, English Literature+ 2 more

English Literature

“About Me I am currently studying English at the University of Exeter. I've taught children from a wide range of age groups before, including my own peers. AS I have studied English, Maths and Biology at A Level and obtained an A in ea...”

About the author

£24 /hr

Bethany H.

Degree: History (Bachelors) - Durham University

Subjects offered:Maths, History+ 1 more


“Experienced, patient and friendly tutor, keen to help with Maths, French and History”

You may also like...

Posts by Bethany

How do you conjugate verbs in the pluperfect tense in French?

How do you substitute a number into an algebraic expression?

Other GCSE Maths questions

How to solve the simultaneous equations 3x+2y=7 and 5x+y=14

If there are 20 marbles in a bag and 1/5 are red, what fraction are red if 1 more red marble is added?

What is the area of triangle ABC where AB = 5 cm, BC = 12 cm and angle ABC = 50 degrees?

Solve the equation 3x^(2)-7x+3 giving your answer to three significant figures.

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss