a^4 - (b+c^4) factorise please
Answers
Answer:
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Answer:
\underline{\mathfrak{\huge{The\:Question:}}}
TheQuestion:
Factorise :- \tt{a^{4} - ( b + c )^{4}}a
4
−(b+c)
4
\underline{\mathfrak{\huge{Your\:Answer:}}}
YourAnswer:
Start with simplifying the equation :-
=》 \tt{a^{4} - ( b + c )^{4}}a
4
−(b+c)
4
Simplify it further :-
=》 \tt{(a^{2})^{2} - ((b+c)^{2})^{2} }(a
2
)
2
−((b+c)
2
)
2
Let ( b + c ) = y
=》 \tt{(a^{2})^{2} - (y^{2})^{2}}(a
2
)
2
−(y
2
)
2
Identity going to be used -
a^{2} - b^{2} = (a-b)(a+b)a
2
−b
2
=(a−b)(a+b)
Use it there :-
=》 \tt{( a^{2} + y^{2} ) ( a^{2} - y^{2} )}(a
2
+y
2
)(a
2
−y
2
)
Again, use the same identity :-
=》 \tt{( a^{2} + y^{2}) ( a + y )( a - y)}(a
2
+y
2
)(a+y)(a−y)
Now, put the value of y = ( b + c )
=》 \tt{( a^{2} + ( b + c)^{2} ) ( a + ( b + c))( a - (b + c))}(a
2
+(b+c)
2
)(a+(b+c))(a−(b+c))
Now, open the brackets :-
=》 \tt{( a^{2} + ( b +c)^{2})( a + b + c )( a - b - c)}(a
2
+(b+c)
2
)(a+b+c)(a−b−c)
Identity to be used -
(a + b)^{2} = a^{2} + b^{2} + 2ab(a+b)
2
=a
2
+b
2
+2ab
Use it and this will be your final step :-
=》 \tt{(a^{2} + b^{2} + c^{2} + 2bc )( a + b + c )( a - b - c )}(a
2
+b
2
+c
2
+2bc)(a+b+c)(a−b−c)
That's your final answer.