What is expand (x+2y)^5 ?

The solution to expand (x+2y)^5 is x^5+10x^4y+40x^3y^2+80x^2y^3+80xy^4+32y^5

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expand (x+2y)^5

expand

(x + 2 y)^{5}

x^{5} + 10 x^{4} y + 40 x^{3} y^{2} + 80 x^{2} y^{3} + 80 x y^{4} + 32 y^{5}

Solution steps

(x + 2 y)^{5}

Apply binomial theorem:

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

a = x, b = 2 y

= i = 0 \sum 5 (i 5) x^{(5 - i)} (2 y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (2 y)^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (2 y)^{1} : 10 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (2 y)^{2} : 40 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (2 y)^{3} : 80 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (2 y)^{4} : 80 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (2 y)^{5} : 32 y^{5}

= x^{5} + 10 x^{4} y + 40 x^{3} y^{2} + 80 x^{2} y^{3} + 80 x y^{4} + 32 y^{5}

lo g_{5} (30) - lo g_{5} (6)

(12 + 9 i) (- 9 - 3 i)

(2 + 3 i) + (6 - 2 i)

- 0. 5^{2}

lo g_{2} (96) + lo g_{2} (32)

What is expand (x+2y)^5 ?
The solution to expand (x+2y)^5 is x^5+10x^4y+40x^3y^2+80x^2y^3+80xy^4+32y^5