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

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

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expand (2w+3)^6

expand

(2 w + 3)^{6}

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

Solution steps

(2 w + 3)^{6}

Apply binomial theorem:

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

a = 2 w, b = 3

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(2 x - y)^{2}

x^{2} y^{2} - x^{2} - 1 + y^{2}

x^{2} y^{2} + x^{2} - y^{2} - 1

(2 x - 8)^{3}

\frac{( \frac{2}{x} + \frac{4}{y} )}{( 2 x + y )}

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