RD Chapter 5 Factorisation of Algebraic Expressions Ex 5.1 Solutions
Question - 11 : - a2 + 4b2 – 4ab – 4c2
Answer - 11 : -
Question - 12 : - x2 – y2 – 4xz + 4z2
Answer - 12 : -
x2 – y2 – 4xz + 4z2
= x2 – 4xz + 4z2 – y2
= (x)2 – 2 x x x 2z + (2z)2 – (y)2
= (x – 2z)2 – (y)2
= (x – 2z + y) (x – 2z – y)
= (x +y – 2z) (x – y – 2z)
Question - 13 : - 
Answer - 13 : -
Question - 14 : - 
Answer - 14 : -
Question - 15 : - 
Answer - 15 : -
Question - 16 : - Give possible expression for the length and breadth of the rectangle having 35y2 + 13y – 12 as its area.
Answer - 16 : -
Area of a rectangle = 35y2 + 13y – 12
= 35y2 + 28y- 15y- 12
(i) If length = 5y + 4, then breadth = 7y – 3
(ii) and if length = 7y-3, then length = 5y+ 4
Question - 17 : - What are the possible expressions for the dimensions of the cuboid whose volume is 3x2 – 12x.
Answer - 17 : -
Volume 3x2 – 12x
= 3x(x – 4)
∴Factors are 3, x, and x – 4
Now, if length = 3, breadth = x and height = x – 4
if length =3, breadth = x – 4, height = x
if length = x, breadth = 3, height = x – 4
if length = x, breadth = x – 4, height = 3
if length = x – 4, breadth = 3, height = x
if length – x – 4, breadth = x, height = 3
Question - 18 : - 
Answer - 18 : -
Question - 19 : - (x + 2) (x2 + 25) – 10x2 – 20x
Answer - 19 : -
(x + 2) (x2 + 25) – 10x2 – 20x
= (x + 2) (x2 + 25) – 10x(x + 2)
= (x + 2) [x2 + 25 – 10x]
= (x + 2) [(x)2 – 2 x x x 5 + (5)2]
= (x + 2) (x – 5)2
Question - 20 : - 2a2 + 26–√ ab +3b2
Answer - 20 : -
2a2 +26–√ ab +3 b2
= (2–√ a)2+ 2–√ ax 3–√ b+(3–√ b)2
= (2–√a+ 3–√ b)2