FACTORISATION & ALGEBRAIC FRACTIONS
EXPANSION Examples: – 4(3 + h) = – 12 – 4h 6q(2p – q) =12pq – 6
= 3 + hk (h – 2k)(3h + k) = 3 – 5hk – 2 – 6hk – 2 3)
(r – 9) = (r – 9)(r – 9) = – 9r = – 18r + 81 – 9r + 81 4)
Example: ① Using HCF + = ( + ) 1) 4 4x + 16 x + 4 FACTORISATION
FACTORISATION Example: ① Using HCF − = ( − ) 2) 9 p 18p - 27pq 2p - 3pq 2 - 3q
FACTORISATION Example: ② Using − = (a+b)(a−b) −9 = − = ( + )( − ) *perfect square*
FACTORISATION Example: ② Using − = (a+b)(a−b) − = − = ( + )( − ) *perfect squares*
FACTORISATION Example: ③Using cross multiplication − − ( − ) ( + ) 7 4 7 4 × × + − − −28 −3 2 =
FACTORISATION Example: ③Using cross multiplication − + =(y−) (y−) 3 5 3 5 × × + − − +15 −8 2 − −
Example: ④ Using common factors in 4 algebraic terms 1) − − + =( − ) + (− + ) = − − ( − ) =( − )( − )
Example: ④ Using common factors in 4 algebraic terms + + + =( + ) + ( + ) = ( + ) + ( + ) =( + )( + )
Examples: 1. − + + + + = − + + + = − + + ALGEBRAIC FRACTIONS
Examples: 2. + − + = − + ( ) x 2 ( ) x 2 + − +
2. − − ÷ ( − ) − = − − − ( − ) = ( + )( − ) ( − ) ( − ) ( − )( − ) = ( + ) ( − ) = + − /