What is expand (1-3x)^5 ?

The solution to expand (1-3x)^5 is 1-15x+90x^2-270x^3+405x^4-243x^5

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expand (1-3x)^5

expand

(1 - 3 x)^{5}

1 - 15 x + 90 x^{2} - 270 x^{3} + 405 x^{4} - 243 x^{5}

Solution steps

(1 - 3 x)^{5}

Apply binomial theorem:

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

a = 1, b = - 3 x

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (- 3 x)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (- 3 x)^{0} : 1

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- 3 x)^{2} : 90 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- 3 x)^{3} : - 270 x^{3}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (- 3 x)^{5} : - 243 x^{5}

= 1 - 15 x + 90 x^{2} - 270 x^{3} + 405 x^{4} - 243 x^{5}

32 - 2

\frac{6}{7} \cdot \frac{1}{2}

1 \cdot \frac{1}{7}

37 (\frac{7}{3})

2.9 9^{2}

What is expand (1-3x)^5 ?
The solution to expand (1-3x)^5 is 1-15x+90x^2-270x^3+405x^4-243x^5