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Popular >

expand (1-x)^4

Solution

expand

(1 - x)^{4}

Solution

1 - 4 x + 6 x^{2} - 4 x^{3} + x^{4}

Solution steps

(1 - x)^{4}

Apply binomial theorem:

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

a = 1, b = - x

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- x)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- x)^{0} : 1

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (- x)^{2} : 6 x^{2}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- x)^{4} : x^{4}

= 1 - 4 x + 6 x^{2} - 4 x^{3} + x^{4}

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Frequently Asked Questions (FAQ)

What is expand (1-x)^4 ?
The solution to expand (1-x)^4 is 1-4x+6x^2-4x^3+x^4