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Popular >

expand (a-1)^4

Solution

expand

(a - 1)^{4}

Solution

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

Solution steps

(a - 1)^{4}

Apply binomial theorem:

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

a = a, b = - 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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