What is expand (3-y)^6 ?

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

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expand (3-y)^6

expand

(3 - y)^{6}

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

Solution steps

(3 - y)^{6}

Apply binomial theorem:

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

a = 3, b = - y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

a \cdot b + (a - 1) \cdot b^{2} + (a - 2) \cdot b^{3}

3 m^{3} b^{2} - 9 b^{3} m^{4}

84 x^{3} + 404 x^{2} + 597 x + 280

1 - a^{6}

\frac{1}{( 2 ) \cdot ( sin ( x ) - cos ( x ) )}

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