What is expand (x-3)^5 ?

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

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expand (x-3)^5

expand

(x - 3)^{5}

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

Solution steps

(x - 3)^{5}

Apply binomial theorem:

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

a = x, b = - 3

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{3}{6}

(2 x - 1) (x + 2)

lo g_{2} (4^{5})

(6 d + 5) - (2 - 3 d)

4 \times 8

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