Factorise algebraic expressions using common factors, grouping, and standard identities like the difference of squares.
Factorising by taking out common factors, or by grouping terms in pairs that share a common factor.
Factorise: 6x²y + 9xy²
3xy(2x+3y)
Factorise by grouping: ax+ay+bx+by
a(x+y)+b(x+y) = (a+b)(x+y)
The difference of squares identity a²−b²=(a+b)(a−b) is one of the most useful factorisation tools.
Factorise: x²−49
(x+7)(x−7)
Factorise: 9x²−16y²
(3x+4y)(3x−4y)
1. Factorise: 4a²b+6ab²
2. Factorise by grouping: px+py+qx+qy
3. Factorise: x²−81
4. Factorise: 25x²−4y²
5. Factorise: x²+8x+16