Expanding a bracket and factorising
See a bracket as a rectangle: expand by painting its area with tiles, then work backwards and find the sides of a rectangle to factorise.
- UK: Year 8
- France: grade 7
- Germany: grade 7
- Iran: grade 8
- Afghanistan: grade 8
- Syria: grade 8
- Palestine: grade 6
- Ukraine: grade 6
- Russia: grade 7
Guide
This studio follows KS3 algebra: multiplying a single term over a bracket, and taking out common factors.
The tiles: a big square is x2, a long strip is x and a small square is 1. A red tile is negative.
3(x + 4) is the area of a rectangle with sides 3 and x + 4. Every part of the bracket is multiplied by 3, so the area is 3x + 12. To expand (brackets) means to write the area as a sum.
To factorise is the other way round: start with the area and find the two sides. The best side on the left is the highest common factor (of an expression) of the terms.
Red times white is red, and red times red is white: −2×−5 = 10.
Paint a block by tapping a tile in the tray, then the block. Build a side with the − and + buttons. Type your answers on the keypad.