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

The solution to expand (3x+2)^4 is 81x^4+216x^3+216x^2+96x+16

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expand (3x+2)^4

expand

(3 x + 2)^{4}

81 x^{4} + 216 x^{3} + 216 x^{2} + 96 x + 16

Solution steps

(3 x + 2)^{4}

Apply binomial theorem:

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

a = 3 x, b = 2

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} \cdot 2^{1} : 216 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} \cdot 2^{2} : 216 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} \cdot 2^{3} : 96 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} \cdot 2^{4} : 16

= 81 x^{4} + 216 x^{3} + 216 x^{2} + 96 x + 16

(m - 2)^{2}

- 7 \cdot 4

2 5^{- 1}

(b + 2) (b - 2)

s (s + 3) (s^{2} + 4 s + 8)

What is expand (3x+2)^4 ?
The solution to expand (3x+2)^4 is 81x^4+216x^3+216x^2+96x+16