Factorise the following:i) x2 – 36ii) 49x2 – 25y2iii) m2 – 12

1.	Factorise the following:i) x2 – 36ii) 49x2 – 25y2iii) m2 – 121iv) 81 – 64x2
Answer» i) x² – 36 = x² – 36 ⇒ (x)² – (6)² is in the form of a² – b² a² – b² = (a + b) (a – b) ∴ x² – 36 = (x + 6) (x – 6) ii) 49x² – 25y² = (7x)² – (5y)² = (7x + 5y) (7x – 5y) iii) m² – 121 = m² -121 = (m)² – (11)² = (m + 11) (m – 11) iv) 81 – 64x² = 81 – 64x² = (9)² – (8x)² = (9 + 8x) (9 – 8x)

Factorise the following:i) x2 – 36ii) 49x2 – 25y2iii) m2 – 121iv) 81 – 64x2

Answer»

i) x² – 36

= x² – 36

⇒ (x)² – (6)² is in the form of a² – b²

a² – b² = (a + b) (a – b)

∴ x² – 36 = (x + 6) (x – 6)

ii) 49x² – 25y²

= (7x)² – (5y)²

= (7x + 5y) (7x – 5y)

iii) m² – 121

= m² -121

= (m)² – (11)²

= (m + 11) (m – 11)

iv) 81 – 64x²

= 81 – 64x²

= (9)² – (8x)²

= (9 + 8x) (9 – 8x)