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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem

Find $(a+b)^4-(a-b)^4$.

$\begin{array}{1 1}(A)\;8ab\\(B)\;8ab(a^2+b^2)\\(C)\;8ab(a+b)\\(D)\;8ab(a^3+b^3)\end{array} $

1 Answer

Toolbox:
  • $(1+x)^n=nC_0+nC_1x+nC_2x^2+.......+nC_1x^r+.....+nC_nx^n$
$(a+b)^x=a^4+4C_1a^3b+4C_2ab^3+4C_4b^4$
$\Rightarrow a^4+4a^3b+6a^2b^2+4ab^3+b^4$-------(1)
$(a-b)^n=a^4+4C_1a^3(-b)+4C_2a^2(-b)^2+4C_3a(-b)^3+4C_4(-b)^4$
$\Rightarrow a^4-4a^3b+6a^2b^2-4ab^3+b^4$-----(2)
$(a+b)^4-(a-b)^4$=Subtracting (2) from (1)
$\Rightarrow 2[4a^3b+4ab^3]$
$\Rightarrow 8ab(a^2+b^2)$
Hence (B) is the correct answer.
answered Jun 23, 2014 by sreemathi.v
 
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