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Popular >

expand (1-a)^4

Solution

expand

(1 - a)^{4}

Solution

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

Solution steps

(1 - a)^{4}

Apply binomial theorem:

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

a = 1, b = - a

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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