What is expand (3y+2)^6 ?

The solution to expand (3y+2)^6 is 729y^6+2916y^5+4860y^4+4320y^3+2160y^2+576y+64

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expand (3y+2)^6

expand

(3 y + 2)^{6}

729 y^{6} + 2916 y^{5} + 4860 y^{4} + 4320 y^{3} + 2160 y^{2} + 576 y + 64

Solution steps

(3 y + 2)^{6}

Apply binomial theorem:

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

a = 3 y, b = 2

= i = 0 \sum 6 (i 6) (3 y)^{(6 - i)} \cdot 2^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} (3 y)^{6} \cdot 2^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (3 y)^{5} \cdot 2^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (3 y)^{4} \cdot 2^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (3 y)^{3} \cdot 2^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (3 y)^{2} \cdot 2^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (3 y)^{1} \cdot 2^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (3 y)^{0} \cdot 2^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (3 y)^{6} \cdot 2^{0} : 729 y^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (3 y)^{5} \cdot 2^{1} : 2916 y^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (3 y)^{4} \cdot 2^{2} : 4860 y^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (3 y)^{3} \cdot 2^{3} : 4320 y^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (3 y)^{2} \cdot 2^{4} : 2160 y^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (3 y)^{1} \cdot 2^{5} : 576 y

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (3 y)^{0} \cdot 2^{6} : 64

= 729 y^{6} + 2916 y^{5} + 4860 y^{4} + 4320 y^{3} + 2160 y^{2} + 576 y + 64

\frac{1}{x - 4} - \frac{1}{x - 3}

(m + 5) (m - 5)

\frac{3}{2} + \frac{5}{3}

(x^{- 1} y)^{3}

e^{x + l n (x + 1)}

What is expand (3y+2)^6 ?
The solution to expand (3y+2)^6 is 729y^6+2916y^5+4860y^4+4320y^3+2160y^2+576y+64