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Collecting like terms

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Expressions, formulae and equations

Collecting like terms

Three red bricks and two blue ones. You can total the reds and total the blues ā€” but you cannot add a red to a blue.

You can total the reds, and total the bluesxxx=3xyy=2y3x + 2ydifferent letters ā†’ different bricks ā†’ cannot be combined
3 apples + 2 oranges is not 5 of anything.

The brick model

A red brick is x cm long and a blue brick is y cm long. Join three red bricks: x + x + x = 3x cm. Join two blue bricks: y + y = 2y cm. Join three red and two blue: 3x + 2y cm. And 3x + 2y will not simplify any further ā€” the bricks are different lengths, so you cannot combine them.

Like terms

LIKE TERMS contain exactly the same letter. You can add, subtract and combine them. 5x + 3x = 8x 7y āˆ’ 2y = 5y 4a + 2a āˆ’ a = 5a Terms with DIFFERENT letters cannot be combined: 3x + 2y stays as 3x + 2y.

Simplifying

To SIMPLIFY an expression, collect the like terms so it is written as shortly as possible. 4x + 3y + 2x + y = (4x + 2x) + (3y + y) = 6x + 4y Deal with each letter separately and you will not go wrong.

Writing terms neatly

Some conventions worth knowing: ā€¢ write a rather than 1a or 1 Ɨ a ā€¢ write 2a rather than a + a ā€¢ write ab rather than a Ɨ b or ba ā€¢ write aĀ² rather than a Ɨ a ā€¢ write aĀ³ rather than a Ɨ a Ɨ a

Worked examples

Simplify 5x + 3x

  1. Both terms have the same letter, so they are like terms.
  2. 5 + 3 = 8.

Answer: 8x

Simplify 7y āˆ’ 2y

  1. Like terms again.
  2. 7 āˆ’ 2 = 5.

Answer: 5y

Simplify 3x + 2y

  1. The letters are different.
  2. Different letters cannot be combined.

Answer: 3x + 2y ā€” it will not simplify

Simplify 4x + 3y + 2x + y

  1. Deal with each letter separately.
  2. x terms: 4x + 2x = 6x.
  3. y terms: 3y + y = 4y.

Answer: 6x + 4y

Simplify 4a + 2a āˆ’ a

  1. All three are like terms.
  2. 4 + 2 āˆ’ 1 = 5.

Answer: 5a

Writing a Ɨ a neatly

  1. A letter multiplied by itself uses an index.
  2. Just as 3 Ɨ 3 is 3Ā².

Answer: aĀ²

Where you see this in real life

  • Adding 3 apples and 2 oranges gives 3 apples and 2 oranges ā€” not 5 of anything. That is exactly why 3x + 2y will not simplify.
  • A bill of 4 coffees and 2 cakes plus 3 more coffees is 7 coffees and 2 cakes: you total each kind separately.

Key words

Like terms
terms containing exactly the same letter
Simplify
rewrite an expression as shortly as possible
Collecting like terms
adding and subtracting the terms that match
Term
one part of an expression, separated by + or āˆ’
Coefficient
the number in front of a letter
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