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Popular >

expand (1+w^2)^4

Solution

expand

(1 + w^{2})^{4}

Solution

1 + 4 w^{2} + 6 w^{4} + 4 w^{6} + w^{8}

Solution steps

(1 + w^{2})^{4}

Apply binomial theorem:

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

a = 1, b = w^{2}

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= 1 + 4 w^{2} + 6 w^{4} + 4 w^{6} + w^{8}

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Frequently Asked Questions (FAQ)

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