Math, asked by akshatyadav1029, 3 months ago

a^4 - (b+c^4) factorise please​

Answers

Answered by SpandanGangurde
0

Answer:

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Answered by aaryasawant306
1

Answer:

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TheQuestion:

Factorise :- \tt{a^{4} - ( b + c )^{4}}a

4

−(b+c)

4

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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.

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