Example 1 — expanding two brackets
Expand and simplify .
- 1Every term in the first bracket multiplies every term in the second — four products in all.
- 2Carry the minus sign with the 5.
- 3
- 4
- 5Collect the two terms: .
Algebra 1
Try each one on paper first, then check a single step. That is worth far more than reading a finished solution.
Example 2 — factorising completely
Factorise completely.
- 1Look for a common factor first: both terms divide by 3.Always the first move.
- 2Check by expanding: and ✓
- 3 is a difference of two squares., with a minus between them.
- 4Stopping at is not 'completely', and that is how the question is always worded.
Example 3 — changing the subject with a square
Make the subject of .
- 1 is multiplied by and squared, so undo those in reverse order.Last operation applied is the first one undone.
- 2Divide both sides by : Undo the multiplication first.
- 3Take the square root of both sides.The opposite of squaring.
- 4The whole fraction is under the root — dividing happened before the root is taken.