What is expand (3a+b^2)^4 ?

The solution to expand (3a+b^2)^4 is 81a^4+108a^3b^2+54a^2b^4+12ab^6+b^8

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expand (3a+b^2)^4

expand

(3 a + b^{2})^{4}

81 a^{4} + 108 a^{3} b^{2} + 54 a^{2} b^{4} + 12 a b^{6} + b^{8}

Solution steps

(3 a + b^{2})^{4}

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) (3 a)^{(4 - i)} (b^{2})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 a)^{4} (b^{2})^{0} : 81 a^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 a)^{3} (b^{2})^{1} : 108 a^{3} b^{2}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 a)^{2} (b^{2})^{2} : 54 a^{2} b^{4}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 a)^{1} (b^{2})^{3} : 12 a b^{6}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 a)^{0} (b^{2})^{4} : b^{8}

= 81 a^{4} + 108 a^{3} b^{2} + 54 a^{2} b^{4} + 12 a b^{6} + b^{8}

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

(a + 2 b)^{3} + (a - 2 b)^{3}

(1 - 2 a)^{3}

55 x^{2} - 3 x + 2582 x^{2} - 9 x^{2615} - 3 x + v + 6

(3 x - 7)^{3}

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