Q. 4 B4.3( 8 Votes )

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Answer :

In expression a4 – (b + c)4


Both terms are perfect square


a4 = a2 × a2


(b + c)4 = (b + c)2 × (b + c)2


a4 – (b + c)4 Seems to be in identity a2-b2 = (a + b)(a-b)


Where a = a2 and b = (b + c)2;


a4 – (b + c)4 = (a2 – (b + c)2)( a2 + (b + c)2),


a2 – (b + c)2 Seems to be in identity a2-b2 = (a + b)(a-b)


Where a = a and b = (b + c);


a2 – (b + c)2 = (a– (b + c))( a+ (b + c)),


a4 – (b + c)4 = (a– (b + c))( a+ (b + c)), ( a2 + (b + c)2)


a4 – (b + c)4 = (a–b–c)(a + b + c), (a2 + b2 + c2 + 2bc)


Hence the factors of a4 – (b + c)4 are (a–b–c),(a + b + c),( a2 + b2 + c2 + 2bc)


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