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Algebraic notation, simplifying and substitution
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In algebra, letters stand for numbers. Learning how to write and simplify expressions is the first big step.
Notation
ab means a × b. 3y means 3 × y, which is y + y + y.
a2 means a × a. ab means a ÷ b.
We write the number first: 5x, not x5.
a2 means a × a. ab means a ÷ b.
We write the number first: 5x, not x5.
Like terms
Like terms have exactly the same letters and powers.
5a + 3b − 2a + b = 3a + 4b
4 × 3m = 12m and x × x × x = x3.
x2 and x are not like terms.
5a + 3b − 2a + b = 3a + 4b
4 × 3m = 12m and x × x × x = x3.
x2 and x are not like terms.
Substitution
Replace each letter with its number and follow the order of operations.
If p = 3 and q = 4: 2(p + q) = 2 × 7 = 14.
If a = −3: a2 = (−3)2 = 9. Use brackets around negatives.
If p = 3 and q = 4: 2(p + q) = 2 × 7 = 14.
If a = −3: a2 = (−3)2 = 9. Use brackets around negatives.
Find the value of 4x + 3 when x = 5.
- Replace x with 5: 4 × 5 + 3
- = 20 + 3
Answer: 23
Letters stand for numbers: 3y means 3 × y. Only like terms can be collected. To substitute, swap letters for numbers and follow BIDMAS.
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