Expressions using Letter-Numbers
Simplifying: like terms
Learn what like terms are, and how to simplify an expression.
The perimeter of a rectangle: length + breadth + length + breadth. With l, b and p: p = l + b + l + b. Swap the terms: l + l + b + b = 2l + 2b.
The two expressions look different but are equal: they give the same value for any l and b. Check with l = 3, b = 4: 3 + 4 + 3 + 4 = 14 and 6 + 8 = 14. We call 2l + 2b the simplified form.
A shop sells pencils at c rupees and erasers at d rupees. Over three days it sells 5, 3 and 10 pencils, and 4, 6 and 1 erasers. Pencil money: 5c + 3c + 10c. That is c added 5 + 3 + 10 times, so 18c (the distributive property). If c = ₹50, that's ₹900.
Erasers: 4d + 6d + 1d = 11d. Total: 18c + 11d.
Can 18c + 11d be shortened? No: c and d are different letters and can't be combined.
- Like terms have the same letter-number(s): 5c, 3c, 10c; or 12n, −4n. They add into one term. The number in front doesn't matter, and 8xy and 9yx are like terms too.
- Unlike terms have different letters, like 18c and 11d. They cannot be combined.
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