Respuesta :

cygnusabc00

Answer:

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

Step-by-step explanation:

Greetings !

Given expression

[tex](x + 9) {}^{5} [/tex]

write 5 as a sum

[tex](x + 9) {}^{3 + 2} [/tex]

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

[tex](x + 9) {}^{3} \times (x + 9) {}^{2} [/tex]

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

[tex](x {}^{3} + 27x {}^{2} + 243x + 729) \times (x + 9) {}^{2} [/tex]

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

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

Finally, simplify the expression gives

[tex]x {}^{5} + 45x {}^{4} + 810x {}^{3} + 7290x {}^{2} + 32805x + 59049[/tex]

Hope it helps!

fieryanswererft

Answer:

[tex]\sf x^5 + 45x^4 + 810x^3 + 7290x^2 + 32805x + 59049[/tex]

Given expression:

[tex]\bf (x+ 9)^5[/tex]

Use Binomial expression to completely simplify the following expression.

Binomial expression formula:

[tex]\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 $}[/tex]

Solving steps:

[tex]\sf \large \text{ $ \sf (x+9)^5 $}[/tex]

expanding:

[tex]\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[/tex]

calculating:

[tex]\sf x^5 + 45x^4 + 810x^3 + 7290x^2 + 32805x + 59049[/tex]

Otras preguntas