(x - 1)^4+ 4(x - 1)^3+ 6(x - 1)^2+ 4(x - 1) + 1 = - Vidyadip

MCQ

$(x - 1)^4+ 4(x - 1)^3+ 6(x - 1)^2+ 4(x - 1) + 1 =$

✓
$x^4$
B
$x^3$
C
$x^2$
D
$1$

✓

Answer

Correct option: A.

$x^4$

Consider the following identity
$ (a+1)^4 $
$ =\left((a+1)^2\right)^2 $
$ =\left(a^2+2 a+1\right)^2 $
$ =a^4+4 a^2+1+4 a^3+4 a+2 a^2 $
$ =a^4+4 a^3+6 a^2+4 a+1 \ldots(i)$
Comparing $i$ with the given question we get
$a=(x-1)$
Therefore
$ (x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1 $
$ =(x-1+1)^4$ from $(i)$
$ =x^4$

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