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Collecting Like Terms

Practise your algebraic simplification skills with this self-marking exercise.

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This is level 3; Quadratic expressions.

Simplify each of the following by collecting together like terms. (do not factorise your answer)

\(4x^2 + 9x + 3x^2\)

Squared Correct Wrong

\(7y + 5y^2 - 2y\)

Squared Correct Wrong

\(6w^2 - 5w - 3w^2\)

Squared Correct Wrong

\(4m + 9m^2 + 8m + 4m^2\)

Squared Correct Wrong

\(3n + 4n^2 - 2n + 4n^2\)

Squared Correct Wrong

\(7a - 6a^2 - 6a - 7a^2\)

Squared Correct Wrong

\(7b^2 + 5c + 3b - 5c\)

Squared Correct Wrong

\(6p + 12p^2 + 8p - 8p^2 - 2p\)

Squared Correct Wrong

\(8d^2 - 2e - 5d^2 + 6e - 4d^2\)

Squared Correct Wrong

\(-9c - 4c^2 - 8c - 8c^2\)

Squared Correct Wrong

\(-14k - 8k^2 - 8k - 13k^2\)

Squared Correct Wrong

\(16n^3 + 16n^2 - 16n^3 + 13n\)

Squared Correct Wrong


This is Collecting Like Terms level 3. You can also try:
Collecting Like Terms Level 1 Collecting Like Terms Level 2 Collecting Like Terms Level 4 Brackets 1 Brackets 2 Brackets 3 Brackets 4 Brackets 5 Brackets 6 Brackets 7 Brackets 8 Brackets 9


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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This activity comprises of five challenges each one requiring you to type in one more fraction than the previous challenge and each starting with a different fraction. The starting fractions are one tenth, one quarter, one third, one half and four sevenths.


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Description of Levels



Level 1 - Collect like terms in basic linear expressions

Example \(7d - 3d\)

Level 2 - Collect like terms in more interesting linear expressions

Example \(5n+4−4n+8\)

Level 3 - Collect like terms in quadratic expressions

Example \(6y+9y^2−3y\)

Level 4 - Collect like terms in Expressions including multiplication and division

Example \(6y+9y\times y−3y^2\)

Brackets Level 1 - Collect like terms when 1 term is repeated

Example: \(5d - (2d + 2)\)

Brackets Level 2 - Collecting like terms when 2 terms are repeated

Example: \((9d - 7) - (5d - 2)\)

Brackets Level 3 - Multiplying a single positive integer over a bracket

Example: \(4(2d + 4)\)

Brackets Level 4 - Multiplying a single negative integer over a bracket

Example: \(-5(5d + 4)\)

Brackets Level 5 - Multiplying a variable over a bracket

Example: \(4d(5d - 5)\)

Brackets Level 6 - Expanding products of two simple binomials

Example: \((d + 7)(d - 2)\)

Brackets Level 7 - Expanding products of two binomials

Example: \((4d + 7)(3d + 2)\)

Brackets Level 8 - Squaring a binomial

Example: \((3d + 2)^2\)

Brackets Level 9 - Simplifying more complex expressions involving brackets

Example: \(5(3d+1)-2(1-2d)\)

Collecting Like Terms

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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