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Popular >

expand (a-2)^4

Solution

expand

(a - 2)^{4}

Solution

a^{4} - 8 a^{3} + 24 a^{2} - 32 a + 16

Solution steps

(a - 2)^{4}

Apply binomial theorem:

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

a = a, b = - 2

= i = 0 \sum 4 (i 4) a^{(4 - i)} (- 2)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} a^{4} (- 2)^{0} : a^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} a^{3} (- 2)^{1} : - 8 a^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} a^{2} (- 2)^{2} : 24 a^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} a^{1} (- 2)^{3} : - 32 a

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} a^{0} (- 2)^{4} : 16

= a^{4} - 8 a^{3} + 24 a^{2} - 32 a + 16

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Frequently Asked Questions (FAQ)

What is expand (a-2)^4 ?
The solution to expand (a-2)^4 is a^4-8a^3+24a^2-32a+16