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

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

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expand (2+3x)^4

expand

(2 + 3 x)^{4}

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

Solution steps

(2 + 3 x)^{4}

Apply binomial theorem:

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

a = 2, b = 3 x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

lo g_{7} (7^{4})

(x - 11) (x + 6)

\frac{- 4}{2}

x^{3} y^{6} - 64

y^{2} + 3 y - 10

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