Algebra
Algebraic expressions
Identify terms and coefficients, collect like terms and evaluate an expression.
An expression is built out of terms, and the + and - signs are the joins between them. In 4x - 9 there are two terms, 4x and -9. The number in front of a letter is its coefficient, so the coefficient of x here is 4 — and a lone letter like y has a coefficient of 1, even though nobody writes the 1.
Like terms, and only like terms
Two terms are alike when they carry exactly the same letters raised to exactly the same powers. 7x and -9x are alike; 4x and 4y are not; 4x and 4xy are not; x and x² are not. Only like terms can be added to or taken from each other, which is why 3x + 5 stays exactly as it is — there is nothing there to collect.
Worked example
Simplify 6a + 4b - 2a + 3b.
Take each sign with the term that follows it: +6a, +4b, -2a, +3b.
The sign in front belongs to the term. Leaving it behind is how a minus quietly turns into a plus.
Finished does not mean short
4a + 7b cannot be made any shorter. An expression is simplified once no two of its terms are alike any more — not once it has become a single term, which most of the time it never will.
Try it together
Now one together: simplify 8p - 3q - 5p + 7q, and then find its value when p = 4 and q = 2.
Collect one letter at a time, and write the whole term — number and letter together — rather than just the number.
1.Collect the p terms. What is 8p - 5p?
Have a go
Have a go on your own: simplify 9k + 2 - 4k.
Hint: Only two of the three terms are alike.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.