What is expand (3-x)^5 ?

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

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expand (3-x)^5

expand

(3 - x)^{5}

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

Solution steps

(3 - x)^{5}

Apply binomial theorem:

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

a = 3, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{3 ( a ^{3} ) ^{4}}{15 a ^{4}}

a + \frac{3}{4}

- 4 \cdot 12

x^{4} - 22 x^{2} - 75

2 (r + 7)

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