Question

Factorize completely 100a² – 25b²​

Answer 1

Step-by-step explanation:

(10a-5b) (10a+5b)

a2 -b2 =( a+b) (a-b)

Answer 2

On factoring 100a² – 25b²​ we will get 25 (2a + b) (2a - b) as factors

Given:

100a² – 25b²​

To find:

Factorize completely 100a² – 25b²​

Solution:

Given equation 100a² – 25b²​

Take 25 as common as shown below

⇒ 25(4a² - b²)

here, 4a² can be written as (2a)²

25(4a² - b²) = 25[(2a)² - b²]

from algebraic identity (a+b)(a-b) = a²-b²

⇒ 25 [ (2a + b) (2a - b) ]

Therefore,

On factoring 100a² – 25b²​ we will get 25 (2a + b) (2a - b) as factors

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