Question

Factorise 36a^2b^2 - 2ab^2c +48 abc^4

Answer 1

Answer:

Step-by-step explanation:

Given : Expression 36a^4 - 97a^2b^2 +36b^436a

4

−97a

2

b

2

+36b

4

To find : Factories the expression ?

Solution :

Expression 36a^4 - 97a^2b^2 +36b^436a

4

−97a

2

b

2

+36b

4

Applying middle term split,

36a^4 - 16a^2b^2-81a^2b^2+36b^436a

4

−16a

2

b

2

−81a

2

b

2

+36b

4

4a^2(9a^2-4b^2)-9b^2(9a^2-4b^2)4a

2

(9a

2

−4b

2

)−9b

2

(9a

2

−4b

2

)

(4a^2-9b^2)(9a^2-4b^2)(4a

2

−9b

2

)(9a

2

−4b

2

)

((2a)^2-(3b)^2)((3a)^2-(2b)^2)((2a)

2

−(3b)

2

)((3a)

2

−(2b)

2

)

Apply identity, a^2-b^2=(a+b)(a-b)a

2

−b

2

=(a+b)(a−b)

(2a+3b)(2a-3b)(3a+2b)(3a-2b)(2a+3b)(2a−3b)(3a+2b)(3a−2b)

The factorization form is

36a^4 - 97a^2b^2 +36b^4=(2a+3b)(2a-3b)(3a+2b)(3a-2b)36a

4

−97a

2

b

2

+36b

4

=(2a+3b)(2a−3b)(3a+2b)(3a−2b)