9a^4+36a^2b^2+36b^4(using appropriate identities)
Answers
36a
4
−97a
2
b
2
+36b
4
=(2a+3b)(2a−3b)(3a+2b)(3a−2b)
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)
#Learn more
Factorise 36a^2 +36a + 9