What is expand (3x-1/2 y)^4 ?

The solution to expand (3x-1/2 y)^4 is (1296x^4+y^4}{16}-54x^3y+\frac{27x^2y^2-3xy^3)/2

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expand (3x-1/2 y)^4

expand

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

\frac{1296 x ^{4} + y ^{4}}{16} - 54 x^{3} y + \frac{27 x ^{2} y ^{2} - 3 x y ^{3}}{2}

Solution steps

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

Apply binomial theorem:

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

a = 3 x, b = - \frac{1}{2} y

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x)^{4} (- \frac{1}{2} y)^{0} : 81 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (- \frac{1}{2} y)^{1} : - 54 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (- \frac{1}{2} y)^{2} : \frac{27 x ^{2} y ^{2}}{2}

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (- \frac{1}{2} y)^{4} : \frac{y ^{4}}{16}

= 81 x^{4} - 54 x^{3} y + \frac{27 x ^{2} y ^{2}}{2} - \frac{3 x y ^{3}}{2} + \frac{y ^{4}}{16}

Join

81 x^{4} - 54 x^{3} y + \frac{27 x ^{2} y ^{2}}{2} - \frac{3 x y ^{3}}{2} + \frac{y ^{4}}{16} : \frac{1296 x ^{4} + y ^{4}}{16} - 54 x^{3} y + \frac{27 x ^{2} y ^{2} - 3 x y ^{3}}{2}

= \frac{1296 x ^{4} + y ^{4}}{16} - 54 x^{3} y + \frac{27 x ^{2} y ^{2} - 3 x y ^{3}}{2}

- x + (x^{2} + 3 x + 2) e^{- x}

\frac{( x + 4 ) ^{2} ( x - 5 )}{( x - 3 ) ( x + 1 ) ( x + 5 )}

4 (\frac{3}{2} - 3 y)

c (2, - 4) y (- 2, - 4) f (- 1, - 4)

\frac{( y + 8 ) ^{2}}{4}

What is expand (3x-1/2 y)^4 ?
The solution to expand (3x-1/2 y)^4 is (1296x^4+y^4}{16}-54x^3y+\frac{27x^2y^2-3xy^3)/2