Multiplication: baβΓdcβ=bdacβ. Factorise and cancel BEFORE multiplying out.
Worked example. xβ3x+2βΓx+2(xβ3)(x+1)β.
- Cancel (x+2) in top with (x+2) in bottom of second.
- Cancel (xβ3) in bottom with (xβ3) in top of second.
- Left with 1x+1β=x+1.
Division: baβΓ·dcβ=baβΓcdβ=bcadβ. 'Flip the second, multiply.'
Worked example. x2+5xx2β4βΓ·x+5xβ2β.
- Flip the second: x2+5xx2β4βΓxβ2x+5β.
- Factorise everything: x(x+5)(xβ2)(x+2)βΓxβ2x+5β.
- Cancel (xβ2) and (x+5).
- Left with xx+2β.
A key Extended-level skill: factorising BEFORE multiplying makes cancellations obvious. If you expand first you'll get a horrendous mess and lose marks.