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Popular >

expand (1+x^2)^4

Solution

expand

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

Solution

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

Solution steps

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

Apply binomial theorem:

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

a = 1, b = x^{2}

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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