factorise: a^4+a^2b^2+b^4
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Answered by
30
a^4+a^2b^2+b^4
= (a^2+b^2)^2. [since , by using first identity which states that a^2+b^2=(a+b)^2]
= (a^2+b^2)^2. [since , by using first identity which states that a^2+b^2=(a+b)^2]
Answered by
53
The given expression is:
+
+
We have to find the factorisation of the given expression.
Solution:
∴ +
+
= +
+
Using the trigonometric identity:
+ 2xy
⇒ =
- 2xy
= - 2
+
= -
= -
Using the trigonometric identity:
= (x + y)(x - y)
= ( + ab)(
- ab)
∴ +
+
= (
+ ab)(
- ab)
Thus, the factorisation of the given expression is
"( + ab)(
- ab)".
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