Web Analytics

Verified Answer :

irspow

the binomial coefficients are 1,5,10,10,5,1     (5/0, 5/1, 4/2, 3/3, 2/4, 1/5)

x^5-25x^4+250x^3-1250x^2+3125x-3125

Answer:

\(x^5-25x^4+250x^3-1250x^2+3125 x-3125\)

Step-by-step explanation:

Here the given expression is,

\((x-5)^5\)

By the binomial theorem,

\((p+q)^n=\sum_{r=0}^{n} ^nC_rp^{n-r} q^r\)

Where,

\(^nC_r=\frac{n!}{(n-r)!r!}\)

Thus, by the above formula,

\((x-5)^5=\sum_{r=0}^{5} ^5C_rx^{5-r} (-5)^r\)

\(=^5C_0x^{5-0} (-5)^0 + ^5C_1x^{5-1} (-5)^1 + ^5C_2x^{5-2} (-5)^2 + ^5C_3x^{5-3} (-5)^3 + ^5C_4x^{5-4} (-5)^4 + ^5C_5x^{5-5} (-5)^5\)

\(=(1)(x^5)(1)+(5)(x^4)(-5)+(10)(x^3)(25)+(10)(x^2)(-125)+(5)(x^1)(625)+(1)(1)(-3125)\)

\(=x^5-25x^4+250x^3-1250x^2+3125 x-3125\)

Related Questions