A term is a part of an expression, which can be a variable or a constant.
Constant – A constant is a value in maths that will never change. e.g., 1, 2, 3, π
Variable – A variable is a value in maths that can change. Its value varies. x, y, z
Like terms are terms that contain the same variables raised to the same powers. Constants are also considered like terms with each other and can be added or subtracted as long as they belong to the same set of numbers (e.g., all real numbers).
When a number is written next to a bracket, it means you multiply the number by everything inside the bracket.
Expanding brackets means multiplying out the expression inside. A helpful way to remember this is FL: First and Last terms.
\( a(b + c) \equiv ab + ac \)
\( a(b - c) \equiv ab - ac \)
The letters represent variables — placeholders for numbers. Refer to the definition on the top. The formula says:
a by ba by cThis works for any numbers. You can substitute numbers in to test it — it will always be true.
The symbol ≡ means "identically equal to": it's always correct, not just sometimes.
Also, remember: when two variables are “stuck” together like ab, it means a × b.
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Now that you know how to expand brackets, remember that you will also have to deal with negatives. This is an important skill to develop.
Just keep in mind:
2 is the same as +2.+a × +b = +ab — multiplying two positive numbers results in a positive number. For example, +2 × +2 = +4.-a × -b = +ab — multiplying two negative numbers results in a positive number (the negatives cancel out). For example, -2 × -2 = +4.-a × +b = -ab — multiplying a negative number by a positive number results in a negative number. For example, -2 × +2 = -4.You can extend this further by changing the operator (multiplication) to other operations like addition or division. The rules for the signs still apply, but it gets trickier.
For example, putting a minus in front can “flip” the results. So -a - -b becomes -a + b or b - a. Just remember: if there is an odd number of minus signs, the result will be negative; otherwise, it will be positive.
Link this to BIDMAS.
Odd number of minus signs → negative result
Even number of minus signs → positive result
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Here is another rule: \(a \times a = a^2\)
This can also be written as a2.
Note - To answer these questions, if you get an \(x^2\) just write it as x^2 or you won't get a point to your score.
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It is just an application of collecting like terms and expanding brackets. Simply expand the brackets first then add or subtract the like terms to simplify the expression.
Again this is an application of the core idea. Suppose that:
\( a(b + c) \equiv ab + ac \)
\( a(b - c) \equiv ab - ac \)
Then if you add another variable, called d, it becomes:
\( a(b + c + d) \equiv ab + ac + ad \)
\( a(b - c + d) \equiv ab - ac + ad\)
\( a(b + c - d) \equiv ab + ac - ad \)
\( a(b - c -d) \equiv ab - ac - ad\)
Just take the key idea you multiply everything inside the bracket by what's outisde the bracket.
Do these questions and mark them honestly with the answers
Note- The final questions require you to think outside the box. It's applying what you learned here to solve an application question.
Expanding brackets involves multiplying each term inside the bracket by the term outside.