Unit 7 · Topic 01 · Algebraic Expressions
Kabir added 3x and 5y and got '8xy.' Anaya said that was as wrong as adding 3 apples and 5 bananas to get 8 apple-bananas.
Once he saw the fruit version, the algebra version stopped being a trick.
You can only really combine things that are actually the same kind of thing.
Ms. Rao wrote 3x + 5y on the board. "Simplify this." Kabir wrote 8xy.
"Let's translate to something you can picture," said Ms. Rao. "x is apples. y is bananas. 3x is 3 apples, 5y is 5 bananas. What do you get if you add 3 apples and 5 bananas?"
"You just... have 3 apples and 5 bananas," said Kabir. "You can't turn them into 8 apple-bananas. They're different things."
"Exactly. 3x and 5y are called UNLIKE terms — different letters, so they can never combine into one term. 3x + 5y simply stays 3x + 5y. That's already its simplest form."
She then wrote 3x + 5x. "Now what?"
Kabir thought fruit again. "3 apples plus 5 apples is 8 apples. So 3x + 5x is 8x?"
"Exactly right. 3x and 5x are LIKE terms — the same letter, so their number parts (called coefficients) simply add together: 3 + 5 = 8, giving 8x."
Anaya tried a mixed one: 4a + 3b + 2a. "There's two different letters mixed together here."
"Group the like terms first," said Ms. Rao. "4a and 2a are like terms — same letter. 3b stands alone, since nothing else has a b."
Anaya regrouped: (4a + 2a) + 3b = 6a + 3b. "That's as simple as it gets — 6a and 3b are unlike terms, so they can't combine any further."
"Adding algebraic expressions is really just this one rule, over and over," said Ms. Rao. "Find the like terms — same letter, same power — add their coefficients, and leave every unlike term exactly as it is."
A term is one piece of an algebraic expression, like 3x, 5y, or 7. Terms with the SAME letter (and same power) are called like terms; terms with different letters are unlike terms.
Like terms can be combined by adding their coefficients (the number in front): 3x + 5x = 8x, because both are 'x' terms.
Unlike terms can NEVER be combined into a single term — 3x + 5y simply stays 3x + 5y, just like 3 apples and 5 bananas stay as two separate counts.
To simplify a longer expression: group the like terms together first, add their coefficients, then write the unlike terms unchanged alongside.
Simplify 5p + 3q + 2p by grouping like terms first.
Explain in your own words why 4m and 4n cannot be added into a single term.
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