RS Aggarwal Class 9 Math Chapter 2 Polynomials Exercise 2F Solution

EXERCISE 2F

Question 1:
25x² – 64y²
= (5x)² – (8y)²
= (5x + 8y) (5x – 8y)

Question 2:
100 – 9x²
= (10)² – (3x)²
= (10 + 3x) (10 – 3x)

Question 3:
5x² – 7y²

Question 4:
(3x + 5y)² – 4z²
= (3x + 5y)² – (2z)²
= (3x + 5y + 2z) (3x + 5y – 2z)

Question 5:
150 – 6x²
= 6 (25 – x²)
= 6 (5² – x²)
= 6 (5 + x) (5 – x)

Question 6:
20x² – 45
= 5(4x² – 9)
= 5 [(2x)² – (3)²]
= 5 (2x + 3) (2x – 3)

Question 7:
3x³ – 48x
= 3x (x² – 16)
= 3x [(x)² – (4)²]
= 3x (x + 4) (x – 4)

Question 8:
2 – 50x²
= 2 (1 – 25x²)
= 2 [(1)² – (5x)²]
= 2 (1 + 5x) (1 – 5x)

Question 9:
27a² – 48b²
= 3 (9a² – 16b²)
= 3 [(3a)² – (4b)²]
= 3(3a + 4b) (3a – 4b)

Question 10:
x – 64x³
= x (1 – 64x²)
= x[(1)² – (8x)²]
= x (1 + 8x) (1 – 8x)

Question 11:
8ab² – 18a³
= 2a (4b² – 9a²)
= 2a [(2b)² – (3a)²]
= 2a (2b + 3a) (2b – 3a)

Question 12:
3a³b – 243ab³
= 3ab (a² – 81 b²)
= 3ab [(a)² – (9b)²]
= 3ab (a + 9b) (a – 9b)

Question 13:
(a + b)³ – a – b
= (a + b)³ – (a + b)
= (a + b) [(a + b)² – 1²]
= (a + b) (a + b + 1) (a + b – 1)

Question 14:
108a² – 3(b – c)²
= 3 [(36a² – (b -c)²]
= 3 [(6a)² – (b – c)²]
= 3 (6a + b – c) (6a – b + c)

Question 15:
x³ – 5x² – x + 5
= x² (x – 5) – 1 (x – 5)
= (x – 5) (x² – 1)
= (x – 5) (x + 1) (x – 1)

Question 16:
a² + 2ab + b² – 9c²
= (a + b)² – (3c)²
= (a + b + 3c) (a + b – 3c)

Question 17:
9 – a² + 2ab – b²
= 9 – (a² – 2ab + b²)
= 3² – (a – b)²
= (3 + a – b) (3 – a + b)

Question 18:
a² – 4ac + 4c² – b²
= a² – 4ac + 4c² – b²
= a² – 2 a 2c + (2c)² – b²
= (a – 2c)² – b²
= (a – 2c + b) (a – 2c – b)

Question 19:
9a² + 3a – 8b – 64b²
= 9a² – 64b² + 3a – 8b
= (3a)² – (8b)² + (3a – 8b)
= (3a + 8b) (3a – 8b) + (3a – 8b)

= (3a – 8b) (3a + 8b + 1)

Question 20:
x² – y² + 6y – 9
= x² – (y² – 6y + 9)
= x² – (y² – 2 y 3 + 3²)
= x² – (y – 3)²
= [x + (y – 3)] [x – (y – 3)]

= (x + y – 3) (x – y + 3)

Question 21:
4x² – 9y² – 2x – 3y
= (2x)² – (3y)² – (2x + 3y)
= (2x + 3y) (2x – 3y) – (2x + 3y)

= (2x + 3y) (2x – 3y – 1)

Question 22:
x⁴ – 1
= (x² )² – 1²
= (x² + 1) (x² – 1)
= (x² + 1) (x + 1) (x – 1)

Question 23:
a – b – a² + b²
= (a – b) – (a² – b²)
= (a – b) – (a – b) (a + b)

= (a – b) (1 – a – b)

Question 24:
x⁴ – 625
= (x²)² – (25)²
= (x² + 25) (x² – 25)

= (x² + 25) (x² – 5²)
= (x² + 25) (x + 5) (x – 5)