Algebraic identities
(a + b)², (a − b)², (a + b)(a − b) with area pictures, and factorising.
Learn with Kutty
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(a + b)² is a square cut into four pieces: a², b² and two ab.
Look: Four pieces: a², ab, ab and b².
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1(x + 5)² = ?
299² = ?
352 × 48 = ?
! Careful!
✗(a + b)² = a² + b².
✓Do not forget the two rectangles: + 2ab.
✗(a − b)² = a² − b².
✓(a − b)² = a² − 2ab + b².
See the whole lesson on one page
(a + b)² is a square cut into four pieces: a², b² and two ab.
So (a + b)² = a² + 2ab + b², not just a² + b². Check with numbers: (1 + 2)² = 9 = 1 + 4 + 4.
Think of it like thisA square garden with side (a + b). Draw two lines and you see a big square, a small square and two equal rectangles.
Solved together
Work out 103² in your head.
103 = 100 + 3. Picture the four pieces.
Add the pieces.
10,000 + 300 + 300 + 9 = 10,609
Answer103² = 10,609.
For older learners and grown-ups: a little more
Three identities: (a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b²; (a + b)(a − b) = a² − b². The last one factorises "difference of two squares": 49x² − 16 = (7x + 4)(7x − 4).
Now practise it
Kanakku makes new questions on algebraic identities every time. It shows the working and gives a hint when you are stuck.