Joining terms of one kind
Pick a 2 by 2 square on a calendar. Add its four dates. Can you name them from the sum alone?
a. Step 1 of 4
- Pick a square. Its top-left date is
a. - The others are
a + 1,a + 7anda + 8. - Add all four dates.
- Join like terms:
4a + 16.
Yes. Subtract 16 from the sum, then divide by 4 to find a.
Like terms — terms with the same letter part.
Rule: join like terms by adding their coefficients. The letter part stays as it is.
Here a + a + a + a = 4a, and 1 + 7 + 8 = 16. At a = 9 the dates are 9, 10, 16 and 17. They add to 52. And 4a + 16 is 4 × 9 + 16 = 36 + 16 = 52. Check back: 52 − 16 = 36, and 36 ÷ 4 = 9.
Taking away works the same way. Take 3a away from 7a. Four a are left: 7a − 3a = 4a.
Slide the square across the calendar. Watch the sum.
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