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}

\frac{1}{x} - 1

\frac{x ^{\frac{3}{2}}}{\frac{3}{2}}

9 \times 4

(p - q)^{3}

\frac{0}{x}

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