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Popular >

expand (2a-2)^4

Solution

expand

(2 a - 2)^{4}

Solution

16 a^{4} - 64 a^{3} + 96 a^{2} - 64 a + 16

Solution steps

(2 a - 2)^{4}

Apply binomial theorem:

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

a = 2 a, b = - 2

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 a)^{3} (- 2)^{1} : - 64 a^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 a)^{2} (- 2)^{2} : 96 a^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 a)^{1} (- 2)^{3} : - 64 a

Simplify

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

= 16 a^{4} - 64 a^{3} + 96 a^{2} - 64 a + 16

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Frequently Asked Questions (FAQ)

What is expand (2a-2)^4 ?
The solution to expand (2a-2)^4 is 16a^4-64a^3+96a^2-64a+16