Undo operations in reverse, doing the same to both sides
Whatever is done to the subject (×, +, square, …) is undone in reverse order, applied to the whole of both sides to keep the equation balanced.
A square is undone by a square root (and vice versa)
To free a squared subject, square root both sides; to free a square-rooted subject, square both sides — square the entire side, not term by term.
If the new subject appears twice, collect and factorise
Gather every term containing the subject on one side, factorise it out, then divide. e.g. from you get .
Drawn from real examiner reports.
Sign errors and mishandling squared terms
When squaring both sides or moving terms across, students drop or flip signs, or square only one term of a side.
Not factorising when the subject appears twice
Students leave the subject in two places and cannot finish; the key step of factorising it out to isolate it is missed.
Trying to cancel across a sum
Cancelling a letter that is added (not a factor of the whole side) — only common factors of the entire side may be cancelled.
Sanity-check with a number
Substitute simple numbers into the original formula and into your rearrangement; they should give the same value.
Changing the subject is just solving for a letter. Undo the operations in reverse order, doing the same to both sides.
Example: make the subject of .
Golden rule of rearranging?
Make the subject of .
