What is expand (x+3y)^5 ?

The solution to expand (x+3y)^5 is x^5+15x^4y+90x^3y^2+270x^2y^3+405xy^4+243y^5

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expand (x+3y)^5

expand

(x + 3 y)^{5}

x^{5} + 15 x^{4} y + 90 x^{3} y^{2} + 270 x^{2} y^{3} + 405 x y^{4} + 243 y^{5}

Solution steps

(x + 3 y)^{5}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = 3 y

= i = 0 \sum 5 (i 5) x^{(5 - i)} (3 y)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (3 y)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (3 y)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (3 y)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (3 y)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (3 y)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (3 y)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (3 y)^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (3 y)^{1} : 15 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (3 y)^{2} : 90 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (3 y)^{3} : 270 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (3 y)^{4} : 405 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (3 y)^{5} : 243 y^{5}

= x^{5} + 15 x^{4} y + 90 x^{3} y^{2} + 270 x^{2} y^{3} + 405 x y^{4} + 243 y^{5}

4 (x + 6)

\frac{12 x ^{8} y}{20 x y ^{4}}

x^{2} \times (- 1)

lo g_{2} (26)

2 x (x - 5)

What is expand (x+3y)^5 ?
The solution to expand (x+3y)^5 is x^5+15x^4y+90x^3y^2+270x^2y^3+405xy^4+243y^5