Q. 4 B4.3( 8 Votes )

# <span lang="EN-US

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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