← LearnYear 7 Maths · AlgebraFree placement check
Year 7AC9M7A02

Simplifying and Substituting

Formulate algebraic expressions using constants, variables, operations and brackets.

A letter stands for a number you do not know yet. Treat it like any other thing you can count.

Builds onYr 6 · Simple algebra: variables

Method

Like terms
3a+5a=8a3a + 5a = 8a
Same letter, so you can add them. Three apples plus five apples.
Unlike terms
3a+5b3a + 5b
Different letters. This will not simplify. Leave it.
Powers count too
3a+5a23a + 5a^{2}
$a$ and $a^{2}$ are not alike. Leave it.
Multiplying
3a×5b=15ab3a \times 5b = 15ab
Multiply the numbers, then write the letters together.

Worked example

e.g. 5a+3b2a+7b5a + 3b - 2a + 7b
  1. Find the like terms. Group them(5a2a)+(3b+7b)(5a - 2a) + (3b + 7b)
  2. Add or subtract each group3a+10b3a + 10b
  3. Check nothing else matches. aa and bb are different, so stop3a+10b3a + 10b

Practice

Simplify:

1
4x+7x4x + 7x
Answer11x11x
2
9y3y9y - 3y
Answer6y6y
3
5a+2b+3a5a + 2b + 3a
Answer8a+2b8a + 2b
4
8m3m+2n8m - 3m + 2n
Answer5m+2n5m + 2n
5
6p+4q2pq6p + 4q - 2p - q
Answer4p+3q4p + 3q
6
3x×4y3x \times 4y
Answer12xy12xy
7
2a+5a2a2a + 5a^{2} - a
Answera+5a2a + 5a^{2}
8
7c+3d7c7c + 3d - 7c
Answer3d3d
9
10k4k+6k10k - 4k + 6k
Answer12k12k
10
Find 3x+2 when x=4\text{Find } 3x + 2 \text{ when } x = 4
Answer1414
11
Find 5y3 when y=6\text{Find } 5y - 3 \text{ when } y = 6
Answer2727
12
Find 2a+3b when a=5,b=2\text{Find } 2a + 3b \text{ when } a = 5, b = 2
Answer1616
Next step
Practise Simplifying and Substituting with instant marking
A free 10-minute placement check finds which Year 7 topics to work on first, then Summit builds a weekly plan around them.
See where my child is →