Sum and Difference of Two Cubes

Ever wondered why some algebra expressions seem impossible to factorise until you spot they're actually cubes in disguise? The sum and difference of cubes have special factorisation patterns that you absolutely need to memorise.

For the sum of cubes, the formula is: a³ + b³ = $a + b$$a² - ab + b²$. Notice how the first bracket uses addition, but the second bracket has that sneaky minus sign between a² and ab.

The difference of cubes works similarly: a³ - b³ = $a - b$$a² + ab + b²$. This time the first bracket uses subtraction, whilst the second bracket has addition between a² and ab.

Top Tip: Remember "SOAP" - Same sign, Opposite sign, Always Positive. The first bracket keeps the same sign as between the cubes, the second bracket starts with the opposite sign, and the last term is always positive!

The key is recognising when you've got cubes hiding in your expression. Numbers like 8, 27, 64 are perfect cubes, and terms like x³, 8y³, or 27z³ should trigger your cube-spotting radar immediately.