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Popular >

expand (1-x)^5

Solution

expand

(1 - x)^{5}

Solution

1 - 5 x + 10 x^{2} - 10 x^{3} + 5 x^{4} - x^{5}

Solution steps

(1 - x)^{5}

Apply binomial theorem:

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

a = 1, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- x)^{2} : 10 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- x)^{3} : - 10 x^{3}

Simplify

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

Simplify

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

= 1 - 5 x + 10 x^{2} - 10 x^{3} + 5 x^{4} - x^{5}

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Frequently Asked Questions (FAQ)

What is expand (1-x)^5 ?
The solution to expand (1-x)^5 is 1-5x+10x^2-10x^3+5x^4-x^5