Question

"Question 3 Factorise the following using appropriate identities:
(i) 9x^2 + 6xy + y^2
(ii) 4y^2 - 4y + 1
(iii) x^2 - y^2/100

Class 9 - Math - Polynomials Page 48"

Answer 1

Identity:

An identity is an equality which is true for all values of a variable in the equality.

(a + b)² = a² + 2ab + b²

In an identity the right hand side expression is called expanded form of the left hand side expression.

 

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Solution:

 (i)  9x² + 6xy + y²

  =(3x)²+(2×3x×y)+ y2

Using identity,

[(a + b)²= a² + 2ab +b² ]

Here, a = 3x & b = y

9x² + 6xy + y²

= (3x)² + (2×3x×y) +y²

 = (3x + y)²

=(3x + y) (3x + y)

 

(ii)  4y² – 4y + 1

= (2y)² –(2×2y×1) +1²

Using identity,

[(a – b)²= a²² –2ab +b² ]

Here, a = 2y & b = 1

4y² – 4y + 1

= (2y)² – (2×2y×1) +1² 

= (2y-1)²

 =(2y – 1) (2y – 1)

iii) x²- y²/100

 = x² – (y/10)²

Using identity,

[a²–b²=(a + b) (a – b)]

Here, a = x & b = (y/10)

x²– y²/100

 = x² – (y/10)² 

= (x– y/10) (x+ y/10)

 

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