Resolve into factors and choose the correct answer : a3+3a2b+3ab2+2b3
Answers
Answer:
Factorise the expression a^3 -3a^2b +3ab^2+2b^3a
3
−3a
2
b+3ab
2
+2b
3
TO FIND :
The factors of the given expression by using factorisation method.
SOLUTION :
Given expression is a^3 -3a^2b +3ab^2+2b^3a
3
−3a
2
b+3ab
2
+2b
3
Now factorise the given expression a^3 -3a^2b +3ab^2+2b^3a
3
−3a
2
b+3ab
2
+2b
3
That is solving the expression a^3 -3a^2b +3ab^2+2b^3a
3
−3a
2
b+3ab
2
+2b
3
as below:
a^3 -3a^2b +3ab^2+2b^3a
3
−3a
2
b+3ab
2
+2b
3
Rewritting the above expression for our convenient to solve it we get,
=a^3 -3a^2b +3ab^2+3b^3-b^3=a
3
−3a
2
b+3ab
2
+3b
3
−b
3
=(a^3 -3a^2b +3ab^2-b^3)+3b^3=(a
3
−3a
2
b+3ab
2
−b
3
)+3b
3
By using the algebraic identity :
(a-b)^3=a^3-3a^2b+3ab^2-b^3(a−b)
3
=a
3
−3a
2
b+3ab
2
−b
3
=(a-b)^3+3b^3=(a−b)
3
+3b
3
∴ a^3 -3a^2b +3ab^2+2b^3=(a-b)^3+3b^3a
3
−3a
2
b+3ab
2
+2b
3
=(a−b)
3
+3b
3
∴ the given expression a^3 -3a^2b +3ab^2+2b^3a
3
−3a
2
b+3ab
2
+2b
3
is factorised into (a-b)^3+3b^3(a−b)
3
+3b
3