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Collecting Like Terms

Practise your algebraic simplification skills with this self-marking exercise.
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This is level 4; Expressions including multiplication and division.

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

\(5x^2 + 3x \times 5x + 4x^2\)

Squared Correct Wrong

\(4 + 3x \times 4x^2 - 12x^3\)

Squared Correct Wrong

\(3x \times 2x - 3x \times 5x\)

Squared Correct Wrong

\( \frac{ 6x^2 + 2x - 3x^2}{ x }\)

Squared Correct Wrong

\( \frac{ 8x^2 + 2x \times 6x}{ 2x }\)

Squared Correct Wrong

\( \frac{ 5x \times 4x + 3x \times 5x }{ 8x - 3x - 4x}\)

Squared Correct Wrong

\(2 \times 2a - 4a^2 \div 4a\)

Squared Correct Wrong

\(3b - 4bc - 2bc^2 + 4b \times c\)

Squared Correct Wrong

\(5de + 2e \times 4d - 2de^2\)

Squared Correct Wrong

\(4f^2 - \frac{g}{2} + 7fg \div 2f\)

Squared Correct Wrong

\(14h \times 10h^2 \div 5h + 16h\)

Squared Correct Wrong

\(\frac{4k^3}{3} \times \frac{6}{k} + \frac{5k}{2} \div \frac{15}{6k}\)

Squared Correct Wrong

Check

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

Instructions

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.
Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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Description of Levels

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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.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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