factorise a⁴ - (a-b)⁴
Answers
Step-by-step explanation:
The factories form is a^4-(a-b)^4=(2a^2+b^2-2ab)(2a-b)(-b)a
4
−(a−b)
4
=(2a
2
+b
2
−2ab)(2a−b)(−b)
Step-by-step explanation:
Given : Expression a^4-(a-b)^4a
4
−(a−b)
4
To find : Factories the expression ?
Solution :
Re-write the expression as,
a^4-(a-b)^4=(a^2)^2-((a-b)^2)^2a
4
−(a−b)
4
=(a
2
)
2
−((a−b)
2
)
2
Using algebraic identity, a^2-b^2=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
a^4-(a-b)^4=(a^2+(a-b)^2)(a^2-(a-b)^2)a
4
−(a−b)
4
=(a
2
+(a−b)
2
)(a
2
−(a−b)
2
)
Again using same identity,
a^4-(a-b)^4=(a^2+a^2+b^2-2ab)(a+(a-b))(a-(a-b))a
4
−(a−b)
4
=(a
2
+a
2
+b
2
−2ab)(a+(a−b))(a−(a−b))
a^4-(a-b)^4=(2a^2+b^2-2ab)(2a-b)(-b)a
4
−(a−b)
4
=(2a
2
+b
2
−2ab)(2a−b)(−b)
Therefore, the factories form is a^4-(a-b)^4=(2a^2+b^2-2ab)(2a-b)(-b)a
4
−(a−b)
4
=(2a
2
+b
2
−2ab)(2a−b)(−b)