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

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

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expand (3x+2y)^4

expand

(3 x + 2 y)^{4}

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

Solution steps

(3 x + 2 y)^{4}

Apply binomial theorem:

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

a = 3 x, b = 2 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{- 13 - i}{3 - 5 i}

\frac{x ^{2} + x - 6}{x ^{2} - 4}

\frac{x}{4 x}

(2 x^{3} - 3 x^{2} + 5 x - 1) - (x^{2} + 1 - 3 x)

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