What is expand (x-3y)^6 ?

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

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expand (x-3y)^6

expand

(x - 3 y)^{6}

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

Solution steps

(x - 3 y)^{6}

Apply binomial theorem:

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

a = x, b = - 3 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

10 \frac{x ^{2}}{y ^{2}} - 1 - 3 \frac{y ^{2}}{x ^{2}}

(x^{- 1} - y^{- 1})^{- 2}

\frac{( 1 + lo g _{2} ( x - 4 ) )}{( lo g _{2} ( x + 3 - x - 3 ) )}

81 a^{4} b^{4} - 256

1.5 x^{4} - 3 x^{3}

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