What is expand (x-3)^6 ?

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

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expand (x-3)^6

expand

(x - 3)^{6}

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

Solution steps

(x - 3)^{6}

Apply binomial theorem:

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

a = x, b = - 3

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(x - 4 x^{2})^{2}

1 7^{2} - 1 5^{2}

(6 x - 7)^{2}

\frac{22 - 14 i}{- 1 + 2 i}

\frac{3}{18}

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