Ever wondered how a market trader keeps her notes short?
Kemi writes down her sales: 3m + 2b + 4m + 5b, where m is a basket of mangoes and b is a bunch of bananas. That's long! She can tidy it to 7m + 7b — and that's exactly what simplifying means.
Revision notes
Collect like terms to make long expressions short and tidy — mangoes with mangoes, bananas with bananas.
Kemi writes down her sales: 3m + 2b + 4m + 5b, where m is a basket of mangoes and b is a bunch of bananas. That's long! She can tidy it to 7m + 7b — and that's exactly what simplifying means.
Terms are the parts of an expression joined by + or −. In 5x + 3y − 2, the terms are 5x, 3y and 2.
Like terms have exactly the same letter part. 3x and 5x are like terms; 3x and 5y are not; x and x2 are not either.
Think of x as mangoes and y as bananas: 3 mangoes + 5 mangoes = 8 mangoes, but 3 mangoes + 5 bananas can't become 8 of one thing.
🔑 Key idea: Only like terms can be added or subtracted.
To simplify 5x + 3 + 2x − 1, collect the x terms: 5x + 2x = 7x. Then collect the numbers: 3 − 1 = 2.
So 5x + 3 + 2x − 1 = 7x + 2. We can't go further, because 7x and 2 are unlike terms.
Each term carries the sign in front of it. In 6y − 4y, the 4y is taken away: 6y − 4y = 2y.
🔑 Key idea: Group like terms, keep each term's sign, then add or subtract the numbers in front.
When terms are multiplied, deal with the numbers first, then the letters: 3 × 4x = 12x and 2x × 5y = 10xy.
A letter times itself is a square: x × x = x2, so 2x × 3x = 6x2.
Adding and multiplying are different: 2x + 3x = 5x, but 2x × 3x = 6x2.
🔑 Key idea: Multiply the numbers, then multiply the letters.
Simplify 7x + 7 + 2x − 5.
Step 1: Group like terms
(7x + 2x) + (7 − 5)
Step 2: Simplify each group
= 9x + 2
Why? Only like terms can be combined: x's with x's, numbers with numbers.
Answer: 9x + 2
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