What does it mean to simplify an expression?

To simplify an expression means rewriting it in its shortest form without changing its value. You add the like terms, those with exactly the same letter part, and combine the plain numbers separately. So 3x + 5 + 2x − 1 becomes 5x + 4. The short version is easier to read, to compare and to use in the next step of a problem.

How do you expand double brackets?

To expand double brackets, multiply each term in the first bracket by each term in the second, then collect like terms. For (x + 3)(x − 4) that gives four products: x², −4x, 3x and −12. The two middle ones add up to −x, which simply means −1x, so the expanded form is x² − x − 12.

How do you remember which products make the x term?

You remember it by asking what each product is made of. A letter times a letter gives x², a letter times a plain number gives an x term, and two plain numbers give a plain number. So in (2x + 5)(3x + 4), only 2x × 4 and 5 × 3x count, and 8x + 15x = 23x.

Why does my child write 3x + 2 as 5x?

Many learners add everything they see, because in arithmetic a sum always ends as one number. But 3x and 2 are different kinds of term, so 3x + 2 is already as short as it gets. Try x = 10 together: 3x + 2 gives 32, while 5x gives 50. Two different results prove that the expressions are not equal.

Can teachers run this algebra expressions game in a lesson at no cost?

Teachers can, since both levels are free in any browser and pupils start without accounts or downloads. For simplify expressions practice, write 2x + 7 + 5x + 3 + x on the board and let pupils race to shorten it to 8x + 10. Then ask who can invent a longer expression with the same result. After that, each pupil fights on a tablet, and the schools plan, priced per student, adds a dashboard of who is improving.

Math practice · reimagined

Algebraic Expressions Game

This algebraic expressions challenge never wants a letter back: you type how many x’s there are, from 7x + 10x up to the x term hidden in (3x + 5)(4x + 7). Count them faster than your rival, and every count becomes a blow.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What is an algebraic expression?

An algebraic expression is a mix of numbers, letters and operation signs, such as 4x + 9, with no equals sign. Unlike an equation, it has nothing to solve: you simplify it, multiply out its brackets or work out its value. If x stands for your age, x + 3 is your age in three years, and 2x is double it.

Every level of Expressions

Example: the x term of (4x + 1)(3x + 8)

Here the game wants only the x coefficient, the number in front of x once the brackets are multiplied out.
Multiply the two outside terms, 4x and 8, to get 32x, then the two middle terms, 1 and 3x, to get 3x.
The other two products, 4x × 3x = 12x² and 1 × 8 = 8, hold no plain x, so leave them out.
Add the two x terms: 32x + 3x = 35x, so you type 35.

Learn it step by step

Algebra starts to feel manageable the moment you realise that x is just a thing you are counting.

Five x plus three x is eight x, for exactly the reason five apples plus three apples is eight apples. The letter names WHAT you have; the number in front — the coefficient — says how many. Adding them changes the count and leaves the thing alone.

Terms that share the same letter are called LIKE terms, and only like terms can be combined. 5x + 3y stays as it is, because apples and pears do not add into a single pile.

So the whole skill here is: find the coefficients, add them, and keep the x. The answer is a number of x's, and it is that number you type.

Tips and common mistakes

Put one bracket along the top of a two-by-two grid and the other down its side, then fill each box. The two x terms always share one diagonal.
A common slip is writing 6x + 4x = 10x². Adding never raises the power; it only changes how many x’s there are, so the sum is 10x.
For combining like terms practice, tip out a pencil case. Call each pen x and each pencil y, then write the pile as one expression, like 3x + 5y.

How to play

Level one shows a sum such as 9x + 12x = ?x, and you type only the number of x’s, 21. Level two is an expanding brackets game in miniature: from (4x + 2)(3x + 4) you type just the x coefficient, 22. Beat your rival to it and Chilli strikes, with your speed turning into extra damage.

— Quick answers —

Expressions: the short FAQ

What does it mean to simplify an expression?: To simplify an expression means rewriting it in its shortest form without changing its value. You add the like terms, those with exactly the same letter part, and combine the plain numbers separately. So 3x + 5 + 2x − 1 becomes 5x + 4. The short version is easier to read, to compare and to use in the next step of a problem.
How do you expand double brackets?: To expand double brackets, multiply each term in the first bracket by each term in the second, then collect like terms. For (x + 3)(x − 4) that gives four products: x², −4x, 3x and −12. The two middle ones add up to −x, which simply means −1x, so the expanded form is x² − x − 12.
How do you remember which products make the x term?: You remember it by asking what each product is made of. A letter times a letter gives x², a letter times a plain number gives an x term, and two plain numbers give a plain number. So in (2x + 5)(3x + 4), only 2x × 4 and 5 × 3x count, and 8x + 15x = 23x.
Why does my child write 3x + 2 as 5x?: Many learners add everything they see, because in arithmetic a sum always ends as one number. But 3x and 2 are different kinds of term, so 3x + 2 is already as short as it gets. Try x = 10 together: 3x + 2 gives 32, while 5x gives 50. Two different results prove that the expressions are not equal.
Can teachers run this algebra expressions game in a lesson at no cost?: Teachers can, since both levels are free in any browser and pupils start without accounts or downloads. For simplify expressions practice, write 2x + 7 + 5x + 3 + x on the board and let pupils race to shorten it to 8x + 10. Then ask who can invent a longer expression with the same result. After that, each pupil fights on a tablet, and the schools plan, priced per student, adds a dashboard of who is improving.

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