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Popular >

expand (1-p)^4

Solution

expand

(1 - p)^{4}

Solution

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

Solution steps

(1 - p)^{4}

Apply binomial theorem:

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

a = 1, b = - p

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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