Question

Find the coefficient of z4 in the expansion of (5+z)8​

Answer 1

Answer:

As expansion is of the form (a+x)^n,so the rth term

a^n-¹ x^r-1 [{n(n-1)(n-2)....(n-r+2)}÷(r-1)!]

z4 will come in 5 th term .

Hence ,we have to find the 5 th term of the expansion .

Here r=5 and n= 8 .

so 5 th term of (5+z)⁸=5⁸–⁵+¹.z⁵–¹

=5⁴.z⁴.70=625×70×4=43750 z⁴

Hence , the co efficient is z⁴ is 43750

Answer 2

Answer:

5x – 4)10 = 10C0 (5x)10–0(–4)0 + 10C1 (5x)10–1(–4)1

+ 10C2 (5x)10–2(–4)2 + 10C3 (5x)10–3(–4)3

+ 10C4 (5x)10–4(–4)4 + 10C5 (5x)10–5(–4)5

+ 10C6 (5x)10–6(–4)6 + 10C7 (5x)10–7(–4)7

+ 10C8 (5x)10–8(–4)8 + 10C9 (5x)10–9(–4)9

+ 10C10 (5x)10–10(–4)10

hope it's help you ☺️☺️☺️

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