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Popular >

expand (1-u^2)^4

Solution

expand

(1 - u^{2})^{4}

Solution

1 - 4 u^{2} + 6 u^{4} - 4 u^{6} + u^{8}

Solution steps

(1 - u^{2})^{4}

Apply binomial theorem:

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

a = 1, b = - u^{2}

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- u^{2})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- u^{2})^{0} : 1

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- u^{2})^{1} : - 4 u^{2}

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- u^{2})^{3} : - 4 u^{6}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- u^{2})^{4} : u^{8}

= 1 - 4 u^{2} + 6 u^{4} - 4 u^{6} + u^{8}

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Frequently Asked Questions (FAQ)

What is expand (1-u^2)^4 ?
The solution to expand (1-u^2)^4 is 1-4u^2+6u^4-4u^6+u^8