(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.

$x^4$

$x^4$

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

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