What is expand (a-3b)^6 ?

The solution to expand (a-3b)^6 is a^6-18a^5b+135a^4b^2-540a^3b^3+1215a^2b^4-1458ab^5+729b^6

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expand (a-3b)^6

expand

(a - 3 b)^{6}

a^{6} - 18 a^{5} b + 135 a^{4} b^{2} - 540 a^{3} b^{3} + 1215 a^{2} b^{4} - 1458 a b^{5} + 729 b^{6}

Solution steps

(a - 3 b)^{6}

Apply binomial theorem:

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

a = a, b = - 3 b

= i = 0 \sum 6 (i 6) a^{(6 - i)} (- 3 b)^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} a^{6} (- 3 b)^{0} : a^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} a^{5} (- 3 b)^{1} : - 18 a^{5} b

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} a^{4} (- 3 b)^{2} : 135 a^{4} b^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} a^{3} (- 3 b)^{3} : - 540 a^{3} b^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} a^{2} (- 3 b)^{4} : 1215 a^{2} b^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} a^{1} (- 3 b)^{5} : - 1458 a b^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} a^{0} (- 3 b)^{6} : 729 b^{6}

= a^{6} - 18 a^{5} b + 135 a^{4} b^{2} - 540 a^{3} b^{3} + 1215 a^{2} b^{4} - 1458 a b^{5} + 729 b^{6}

(x^{5} - \frac{1}{4 x ^{5}})^{2}

\frac{x ^{2} + 3 x - 4}{x + 4}

\frac{25}{125}

\frac{tan ^{2} ( θ ) + 1}{tan ( θ ) csc ^{2} ( θ )}

(2 x - y)^{7}

What is expand (a-3b)^6 ?
The solution to expand (a-3b)^6 is a^6-18a^5b+135a^4b^2-540a^3b^3+1215a^2b^4-1458ab^5+729b^6