Question

find the common factor using identities ​

Answer 1

Answer:

x - 2y

Step-by-step explanation:

Formulae used :

1. a^2 - b^2 = ( a + b )( a - b )
2. a^2 - 2ab + b^2 = ( a - b )^2

Using the first one for factorising x^2 - 4y^2

= > ( x )^2 - ( 2y )^2

= > ( x + 2y )( x - 2y )

Using the second one for factorising x^2 - 4xy + 4y^2

= > ( x )^2 - 2( 2xy ) + ( 2y )^2

= > ( x - 2y )^2

= > ( x - 2y )( x - 2y )

Since x - 2y is common in both the results, x - 2y is the required common factor.

Answer 2

Question :--- Find the common Factor between x² - 4y² and x² -4xy + 4y² using the identities ?

Identity used :--

→ x² - y² = (x+y)(x-y)

→ x² - 2xy + y² = (x-y)²

______________________

Solution :---

→ x² - 4y² can be written as

→ (x)² - (2y)²

Now, using x² - y² = (x+y)(x-y) we get,

→ (x+2y)(x-2y) ----------- Equation (1)

_______________________

Similarly,

→ x² -4xy + 4y² can be written as

→ (x)² - 2*x*2y + (2y)²

Now , using x² - 2xy + y² = (x-y)² we get,

→ (x-2y)²

→ (x-2y)(x-2y) --------------- Equation (2) .

_________________________

So, Common Factor From Equation (1) and Equation (2) ,

→ (x+2y)(x-2y) and (x-2y)(x-2y) is (x-2y) .

Hence, Required Common Factor is (x-2y).