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}

45 p^{2}

(12 x^{2} - 8 x - 15) m^{2}

(x^{- 1})^{- 1}

\frac{( n + 1 ) !}{( n - 1 ) !}

8 \cdot \frac{1}{8}

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