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

The solution to expand (x^2+3)^6 is x^{12}+18x^{10}+135x^8+540x^6+1215x^4+1458x^2+729

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expand (x^2+3)^6

expand

(x^{2} + 3)^{6}

x^{12} + 18 x^{10} + 135 x^{8} + 540 x^{6} + 1215 x^{4} + 1458 x^{2} + 729

Solution steps

(x^{2} + 3)^{6}

Apply binomial theorem:

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

a = x^{2}, b = 3

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

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (x^{2})^{6} \cdot 3^{0} : x^{12}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (x^{2})^{5} \cdot 3^{1} : 18 x^{10}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (x^{2})^{4} \cdot 3^{2} : 135 x^{8}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (x^{2})^{3} \cdot 3^{3} : 540 x^{6}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (x^{2})^{2} \cdot 3^{4} : 1215 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (x^{2})^{1} \cdot 3^{5} : 1458 x^{2}

Simplify

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

= x^{12} + 18 x^{10} + 135 x^{8} + 540 x^{6} + 1215 x^{4} + 1458 x^{2} + 729

\frac{32}{3}

8 x^{3} + z^{3}

\frac{( c ^{2} + 2 c - 35 )}{( c - 5 )}

(9 m + 4 n)^{2}

\frac{12}{18}

What is expand (x^2+3)^6 ?
The solution to expand (x^2+3)^6 is x^{12}+18x^{10}+135x^8+540x^6+1215x^4+1458x^2+729