Question

3. Factorise the following using appropriate identities:
(1) 9x + xy + y
(ii) 4y - 4y + 1​

Answer 1

Answer:

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)

#Pari here...