Question

factorise a^4-(b+c)^4​

Answer 1

$\underline{\mathfrak{\huge{The\:Question:}}}$

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

$\underline{\mathfrak{\huge{Your\:Answer:}}}$

Start with simplifying the equation :-

=》 $\tt{a^{4} - ( b + c )^{4}}$

Simplify it further :-

=》 $\tt{(a^{2})^{2} - ((b+c)^{2})^{2} }$

Let ( b + c ) = y

=》 $\tt{(a^{2})^{2} - (y^{2})^{2}}$

Identity going to be used -

$a^{2} - b^{2} = (a-b)(a+b)$

Use it there :-

=》 $\tt{( a^{2} + y^{2} ) ( a^{2} - y^{2} )}$

Again, use the same identity :-

=》 $\tt{( a^{2} + y^{2}) ( a + y )( a - y)}$

Now, put the value of y = ( b + c )

=》 $\tt{( a^{2} + ( b + c)^{2} ) ( a + ( b + c))( a - (b + c))}$

Now, open the brackets :-

=》 $\tt{( a^{2} + ( b +c)^{2})( a + b + c )( a - b - c)}$

Identity to be used -

$(a + b)^{2} = a^{2} + b^{2} + 2ab$

Use it and this will be your final step :-

=》 $\tt{(a^{2} + b^{2} + c^{2} + 2bc )( a + b + c )( a - b - c )}$

That's your final answer.

Answer 2

7QUESTIONS :)

$factorise a^4-(b+c)^44$

$ANSWER$

Start with simplifying the equation :-

=》 \tt{a^{4} - ( b + c )^{4}}a

4

−(b+c)

Simplify it further :-

=》 \tt{(a^{2})^{2} - ((b+c)^{2})^{2} }(a

2

−((b+c)

Let ( b + c ) = y

=》 \tt{(a^{2})^{2} - (y^{2})^{2}}(a

Identity going to be used -

a^{2} - b^{2} = (a-b)(a+b)a

=(a−b)(a+b)

Use it there :-

=》 \tt{( a^{2} + y^{2} ) ( a^{2} - y^{2} )}(a

Again, use the same identity :-

=》 \tt{( a^{2} + y^{2}) ( a + y )( a - y)}(a

)(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

)(a+b+c)(a−b−c)

Identity to be used -

(a + b)^{2} = a^{2} + b^{2} +

Use it and this will be your final step :-

=》 \tt{(a^{2} + b^{2} + c^{2} + 2bc )( a + b + c )( a - b - c )}(a

+2bc)(a+b+c)(a−b−