What is expand (6-1/2 a)^6 ?

The solution to expand (6-1/2 a)^6 is 46656-23328a+4860a^2-540a^3+(135a^4)/4-(9a^5)/8+(a^6)/(64)

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expand (6-1/2 a)^6

expand

(6 - \frac{1}{2} a)^{6}

46656 - 23328 a + 4860 a^{2} - 540 a^{3} + \frac{135 a ^{4}}{4} - \frac{9 a ^{5}}{8} + \frac{a ^{6}}{64}

Solution steps

(6 - \frac{1}{2} a)^{6}

Apply binomial theorem:

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

a = 6, b = - \frac{1}{2} a

= i = 0 \sum 6 (i 6) \cdot 6^{(6 - i)} (- \frac{1}{2} a)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 6^{6} (- \frac{1}{2} a)^{0} : 46656

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 6^{5} (- \frac{1}{2} a)^{1} : - 23328 a

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 6^{4} (- \frac{1}{2} a)^{2} : 4860 a^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 6^{3} (- \frac{1}{2} a)^{3} : - 540 a^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 6^{2} (- \frac{1}{2} a)^{4} : \frac{135 a ^{4}}{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 6^{1} (- \frac{1}{2} a)^{5} : - \frac{9 a ^{5}}{8}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 6^{0} (- \frac{1}{2} a)^{6} : \frac{a ^{6}}{64}

= 46656 - 23328 a + 4860 a^{2} - 540 a^{3} + \frac{135 a ^{4}}{4} - \frac{9 a ^{5}}{8} + \frac{a ^{6}}{64}

\frac{cos ( x )}{1 - sin ( x )} + \frac{cos ( x )}{1 + sin ( x )}

\frac{csc ^{2} ( x ) - cot ^{2} ( x )}{sin ( - x ) cot ( x )}

(y + 3) (y^{2} - 3 y + 9)

- 5 x + 5 x

3^{4} \cdot 5^{6}

What is expand (6-1/2 a)^6 ?
The solution to expand (6-1/2 a)^6 is 46656-23328a+4860a^2-540a^3+(135a^4)/4-(9a^5)/8+(a^6)/(64)