Question

factorize 25/4x^2-y^2/9

Answer 1

Answer-

Q. Factorize 25x²/4 - y²/9

Solution- We can write 25x²/4 - y²/9 as (5x/2)²- (y/3)²

[We need to convert the 2 terms in the form of 2 whole squares so that we can apply the suitable algebraic identity.]

By using the algebraic identity a²-b²= (a+b) (a-b)

where a= 5x/2 and b= y/3

⇒ (5x/2+ y/3) (5x/2- y/3)

∴ 25x²/4 - y²/9= (5x/2+ y/3) (5x/2- y/3)

Answer 2

Answer:

Step-by-step explanation:

25−4x225-4x2

Rewrite 2525 as 5252.

52−4x252-4x2

Rewrite 4x24x2 as (2x)2(2x)2.

52−(2x)252-(2x)2

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b) where a=5a=5 and b=2xb=2x.

(5+2x)(5−(2x))(5+2x)(5-(2x))

Multiply 22 by −1-1.

(5+2x)(5−2x)