Key ideas
Like terms
Like terms have exactly the same letter. Group the tiles that match.
x + x + x + 1 + 1 = 3x + 2
3x and 2 are not like terms, so 3x + 2 can't be simplified.
Multiplying
Multiply the numbers, then write the letters together.
3 × 4a = 12a
2a × 5b = 10ab
a × a = a²
Expanding a bracket
Multiply every term inside by the term outside. Use a grid.
| x | +4 | |
| 3 | 3x | +12 |
Substitution
Replace each letter with its number, then use BODMAS.
If a = 4: 3a + 2 = 3 × 4 + 2 = 14
Typing answers: type 5x + 3 or 4a + 2b. For a square, use the ² button or type ^2. Check the preview under the box.
Collecting like terms (one letter)
Simplify 2x + 3 + 4x + 1.(2 marks)
Show it with tiles.
In plain EnglishEach x tile is one x. Each small yellow tile is 1.
Group the like tiles.2x + 4x = 6x x tiles3 + 1 = 4 unit tiles✓1= 6x + 4✓2
In plain EnglishPut the x tiles together and the unit tiles together.
Collecting like terms (two letters)
Simplify 3a + 2b + a + 4b.(2 marks)
Group the a terms and the b terms.3a + a = 4a✓12b + 4b = 6b
In plain Englisha on its own means 1a. a terms and b terms are not like terms, so they stay separate.
Write the answer.= 4a + 6b✓2
In plain EnglishWrite the a terms and the b terms together. You cannot add 4a and 6b, so leave them as they are.
⚠ A common mistake: writing 10ab. a and b are different, so 4a + 6b can't be added together.
Multiplying expressions
Simplify (a) 3 × 5x (b) 2a × 4b (c) y × y.(3 marks)
A number times a term.3 × 5x = 15x✓1
In plain EnglishMultiply the numbers: 3 × 5 = 15. The x stays.
Two terms.2a × 4b = 2 × 4 × a × b = 8ab✓2
In plain EnglishMultiply the numbers, then write the letters next to each other, in alphabetical order.
The same letter twice.y × y = y²✓3
In plain Englishy times itself is y squared.
Expanding a single bracket
Expand 5(x + 3).(2 marks)
Grid.
| x | +3 | |
| 5 |
In plain EnglishWrite 5 down the side and the two terms in the bracket along the top.
Multiply.
= 5x + 15✓2
| x | +3 | |
| 5 | 5x | +15 |
In plain English5 × x = 5x and 5 × 3 = 15.
⚠ A common mistake: 5x + 3. The 5 multiplies everything in the bracket.
Number machines
What comes out of this machine when 7 goes in?(1 mark)
Follow the arrows.7 × 3 = 2121 − 4 = 17✓1
In plain EnglishDo each step in order, from left to right.
The output of the machine is 26. What was the input?(2 marks)
Start at the end and do the opposite.26 − 2 = 24 opposite of + 2
In plain EnglishGo backwards through the machine, doing the inverse of each step.
Undo the × 4.244 = 6✓2Check: 6 × 4 + 2 = 26 ✓
In plain EnglishThe opposite of × 4 is ÷ 4.
Substitution
If a = 4 and b = 7, find the value of 3a + b.(2 marks)
Replace the letters.3 × 4 + 7✓1
In plain English3a means 3 × a.
Work it out.= 12 + 7 = 19✓2
In plain EnglishMultiply first, then add.
Substitution into formulae
The cost, C pounds, of hiring a bike for h hours is C = 5h + 8. Find the cost of hiring a bike for 3 hours.(2 marks)
Substitute.C = 5 × 3 + 8✓1
In plain EnglishReplace h with 3.
Calculate.C = 15 + 8 = £23✓2
In plain EnglishMultiply before you add: 5 × 3 = 15, then add the 8. The answer is a cost, so write £.
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Your turn
Type expressions like 5x + 3 and check the preview under the box. Stuck? Tap Need a hint?