What is expand (3x^2+1)^4 ?

The solution to expand (3x^2+1)^4 is 81x^8+108x^6+54x^4+12x^2+1

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expand (3x^2+1)^4

expand

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

81 x^{8} + 108 x^{6} + 54 x^{4} + 12 x^{2} + 1

Solution steps

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

Apply binomial theorem:

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

a = 3 x^{2}, b = 1

= i = 0 \sum 4 (i 4) (3 x^{2})^{(4 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x^{2})^{4} \cdot 1^{0} : 81 x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x^{2})^{3} \cdot 1^{1} : 108 x^{6}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x^{2})^{2} \cdot 1^{2} : 54 x^{4}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x^{2})^{1} \cdot 1^{3} : 12 x^{2}

Simplify

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

= 81 x^{8} + 108 x^{6} + 54 x^{4} + 12 x^{2} + 1

\frac{1}{4} \times (- 6)

\frac{1}{4} \times 60

3 6 - 46

m^{2} + 6 m + 8

x^{- 1} + x^{- 1}

What is expand (3x^2+1)^4 ?
The solution to expand (3x^2+1)^4 is 81x^8+108x^6+54x^4+12x^2+1