What is expand (3x-y)^5 ?

The solution to expand (3x-y)^5 is 243x^5-405x^4y+270x^3y^2-90x^2y^3+15xy^4-y^5

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expand (3x-y)^5

expand

(3 x - y)^{5}

243 x^{5} - 405 x^{4} y + 270 x^{3} y^{2} - 90 x^{2} y^{3} + 15 x y^{4} - y^{5}

Solution steps

(3 x - y)^{5}

Apply binomial theorem:

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

a = 3 x, b = - y

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} (- y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} (- y)^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} (- y)^{1} : - 405 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} (- y)^{2} : 270 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} (- y)^{3} : - 90 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} (- y)^{4} : 15 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} (- y)^{5} : - y^{5}

= 243 x^{5} - 405 x^{4} y + 270 x^{3} y^{2} - 90 x^{2} y^{3} + 15 x y^{4} - y^{5}

x^{3} - 6 x + 9

x^{3} - 6 x + 5

25 \cdot 25 \cdot 25

\frac{2}{5} \times \frac{7}{2}

\frac{2}{5} \times \frac{7}{9}

What is expand (3x-y)^5 ?
The solution to expand (3x-y)^5 is 243x^5-405x^4y+270x^3y^2-90x^2y^3+15xy^4-y^5