Multiplying binomials and identities
Multiply two brackets as a rectangle of tiles and on a grid, see why (a + b)² has two ab strips, and tell an identity from an equation.
- UK: Year 9
- France: grade 9
- Germany: grade 7
- Iran: grade 9
- Afghanistan: grade 8
- Syria: grade 8
- Palestine: grade 8
- Ukraine: grade 7
- Russia: grade 7
Guide
This studio follows KS3 algebra (expanding products of two binomials) and GCSE A6: the difference between an equation and an identity.
(x + 3)(x + 2) is the area of a rectangle with sides x + 3 and x + 2. Every term of one bracket multiplies every term of the other: four blocks.
The grid (box) method is the same rectangle without the tiles: the terms of one bracket down the side, the other along the top, and each cell is a product.
(a + b)2 = a2 + 2ab + b2: the big square has an a2, a b2 and two ab strips. (a + b)(a − b) = a2 − b2: the middle strips cancel.
An identity is true for every value of the letters; an equation is true only for some. One value that works does not prove an identity, but one value that fails disproves it.
Paint a block by tapping a tile, then the block. In the grid, tap a cell and type on the keypad.