Question

Please help me with my homework f{(x+9)^5}" alt="\bf{(x+9)^5}" align="absmiddle" class="latex-formula">

Thank you

Answer 1

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:

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

Solving steps:

$\sf \large \sf (x+9)^5$

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:

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

Answer 2

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!