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White raven [17]
2 years ago
12

Please help me with my homework

f{(x+9)^5}" alt="\bf{(x+9)^5}" align="absmiddle" class="latex-formula">

Thank you
Mathematics
2 answers:
Sidana [21]2 years ago
8 0

Answer:

\sf x^5 + 45x^4 + 810x^3 + 7290x^2  + 32805x + 59049

Given expression:

\bf (x+ 9)^5

Use Binomial expression to completely simplify the following expression.

Binomial expression formula:

\sf \large \text{ $  \sf (x+y)^n =  \  ^n C_0 x^n y^0 + ^n C_1 x^{n-1} y^1+^n C_2 x^{n-2} y^2 +...  + ^n C_n x^0 y^n $}

Solving steps:

\sf \large \text{ $  \sf (x+9)^5  $}

expanding:

\sf  \  ^5 C_0 (x)^5 (9)^0 + ^5 C_1 (x)^{5-1} (9)^1+ ^5 C_2 x^{5-2} (9)^2 +^5 C_3 x^{5-3} (9)^3 +^5 C_4 x^{5-4} (9)^4  + ^5 C_5 x^{5-5} (9)^5

calculating:

\sf x^5 + 45x^4 + 810x^3 + 7290x^2  + 32805x + 59049

Brut [27]2 years ago
3 0

Answer:

x⁵+ 45x⁴+ 810x³+ 7290x²+ 32805x +59049

Step-by-step explanation:

Greetings !

Given expression

(x + 9) {}^{5}

write 5 as a sum

(x + 9) {}^{3 + 2}

use \: a {}^{m + n}  = a {}^{m}  \times a {}^{n} to \: expand \: the \: expression.

(x + 9) {}^{3}  \times (x + 9) {}^{2}

Use (a+b)³=a³+3a²b+b³ to expand the expression

(x {}^{3}  + 27x {}^{2}  + 243x + 729) \times (x + 9) {}^{2}

Use (a+b)²=a²+2ab+b² to the second expression to expand it

(x {}^{3}  + 27x {}^{2}  + 243x + 729) \times(x {}^{2}  + 18x + 81)

Finally, simplify the expression gives

x {}^{5}  + 45x {}^{4}  + 810x {}^{3}  + 7290x {}^{2}  + 32805x + 59049

Hope it helps!

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