If the sum and difference of two expressions are 5a2 – a – 4and a2

1.	If the sum and difference of two expressions are 5a2 – a – 4and a2 + 9a – 10 respectively, then what is their LCM ?
Answer» Let P and Q be the two expressions. Then, P + Q = 5a² – a – 4 ...(i) P – Q = a² + 9a – 10 ...(ii) Adding (i) and (ii) ⇒ 2P = 6a² + 8a – 14 ⇒ P = 3a² + 4a – 7 = (a – 1) (3a + 7) From (i), Q = (5a² – a – 4) – (3a² + 4a – 7) = 2a² – 5a + 3 = (a – 1) (2a – 3) ∴ LCM of P and Q = (a – 1) (2a – 3) (3a + 7).

If the sum and difference of two expressions are 5a2 – a – 4and a2 + 9a – 10 respectively, then what is their LCM ?

Answer»

Let P and Q be the two expressions. Then,

P + Q = 5a² – a – 4 ...(i)

P – Q = a² + 9a – 10 ...(ii)

Adding (i) and (ii)

⇒ 2P = 6a² + 8a – 14 ⇒ P = 3a² + 4a – 7 = (a – 1) (3a + 7)

From (i), Q = (5a² – a – 4) – (3a² + 4a – 7) = 2a² – 5a + 3 = (a – 1) (2a – 3)

∴ LCM of P and Q = (a – 1) (2a – 3) (3a + 7).