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

Ruadhan P.

Degree: Physics (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

-Personal Statements-

“I am a currently studying Physics at the University of Nottingham. The way Physics and Maths are able to explain the Universe around us truly fascinates me and I hope to be able to share that fascination and excitement for the subject...”

£18 /hr

Jakub C.

Degree: PPE (Bachelors) - Durham University

Subjects offered:Maths, Politics+ 3 more

-Personal Statements-

“Hi, my name is Jakub, I graduated from Durham in PPE last year and I moved further up north to Edinburgh, where I am currently studying masters in Public Policy”

MyTutor guarantee

£18 /hr

Charuka W.

Degree: Chemical engineering (Masters) - Birmingham University

Subjects offered:Maths


“3rd Year Chemical engineering student with tutoring experience in maths, dedicated to help your son or daughter reach their full potential in maths. ”

MyTutor guarantee

About the author

£22 /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

expand the brackets (x+5)(x+3) furthermore what are the two values of x

How do you use the pythagoras equation?

Solve the simultaneous equations: 2x + 3y = 28 and x + y = 11

Find the volume and surface area of a cylinder, of length 20cm and radius 5cm.

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