# 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)

 $$4x^2 + 2x \times 3x + 4x^2$$ $$2 + 2x \times 3x^2 - 6x^3$$ $$3x \times 3x - 2x \times 3x$$ $$\frac{ 5x^2 + 2x - 3x^2}{ x }$$ $$\frac{ 8x^2 + 8x \times 6x}{ 2x }$$ $$\frac{ 5x \times 4x + 4x \times 2x }{ 8x - 3x - 4x}$$ $$4 \times 4a - 4a^2 \div 4a$$ $$3b - 4bc - 5bc^2 + 4b \times c$$ $$4de + 3e \times 4d - 5de^2$$ $$5f^2 - \frac{g}{2} + 11fg \div 2f$$ $$14h \times 6h^2 \div 3h + 19h$$ $$\frac{4k^3}{3} \times \frac{6}{k} + \frac{5k}{2} \div \frac{15}{6k}$$
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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.

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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.

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