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

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

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expand (2x+3y)^4

expand

(2 x + 3 y)^{4}

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

Solution steps

(2 x + 3 y)^{4}

Apply binomial theorem:

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

a = 2 x, b = 3 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

208 - 0.7 (40)

\frac{2}{2} + \frac{3}{2}

(3 a^{2} - 3 b c^{2} + 4 b c) - (- 8 a^{2} + 5 b c)

(y + 11)^{2}

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