Factorisation and Algebraic Fractions

Question 12:    Diagram shows a square ABCD and a right-angled triangle PQR with equal area. Based on the information, find the value of x. Hence, find the perimeter, in cm, of the square ABCD. [4 marks]   Solution: ( 3 x + 2 ) 2 = 1 2 ( 4 x + 8 ) 4 … Read more

Question 9: (a) Factorise 12×2 – 27y2 (b)   Simplify 3 m 2 − 10 m + 3 m 2 − 9 ÷ 3 m − 1 m + 3 .   Solution: (a) 12×2 – 27y2 = 3 (4×2 – 9y2) = 3(2x – 3y) (2x + 3y) (b) 3 m 2 − 10 m + … Read more

Question 5: (a) Simplify: (m – 4n)(m + 4n) – m2 (b) Simplify: 3 x − 3 y x + y × 2 x + 2 y 6 x   Solution: (a) (m – 4n)(m + 4n) – m2 = m2 + 4mn – 4mn – 4n2 – m2 = 0   (b) 3 x − 3 … Read more

2.2.1 Factorisation and Algebraic Fractions, PT3 Practice Question 1: (a)(i) Factorise 18a + 3 (a)(ii) Expand –3 (–y + 5) (b) Express 5 6 y − 3 x − 5 12 y as a single fraction in its simplest form. Solution: (a)(i) 18a + 3 = 3(6a + 1)   (a)(ii) –3 (–y + 5) = 3y … Read more

2.1 Factorisation and Algebraic Fractions 2.1.1 Expansion 1. The product of an algebraic term and an algebraic expression: a(b + c) = ab + ac  a(b – c) = ab – ac 2. The product of an algebraic expression and another algebraic expression: (a + b) (c + d)  = ac + ad + bc + bd … Read more