What is expand (6x-4y)^4 ?

The solution to expand (6x-4y)^4 is 1296x^4-3456x^3y+3456x^2y^2-1536xy^3+256y^4

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expand (6x-4y)^4

expand

(6 x - 4 y)^{4}

1296 x^{4} - 3456 x^{3} y + 3456 x^{2} y^{2} - 1536 x y^{3} + 256 y^{4}

Solution steps

(6 x - 4 y)^{4}

Apply binomial theorem:

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

a = 6 x, b = - 4 y

= i = 0 \sum 4 (i 4) (6 x)^{(4 - i)} (- 4 y)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (6 x)^{4} (- 4 y)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (6 x)^{3} (- 4 y)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (6 x)^{2} (- 4 y)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (6 x)^{1} (- 4 y)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (6 x)^{0} (- 4 y)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (6 x)^{4} (- 4 y)^{0} : 1296 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (6 x)^{3} (- 4 y)^{1} : - 3456 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (6 x)^{2} (- 4 y)^{2} : 3456 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (6 x)^{1} (- 4 y)^{3} : - 1536 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (6 x)^{0} (- 4 y)^{4} : 256 y^{4}

= 1296 x^{4} - 3456 x^{3} y + 3456 x^{2} y^{2} - 1536 x y^{3} + 256 y^{4}

(1 + a) (1 - b)

25 x^{4} y^{2} - 64 w^{10} z^{14}

\frac{8}{7} - \frac{3}{8}

- 5 x^{2} - 2 x + 7

What is expand (6x-4y)^4 ?
The solution to expand (6x-4y)^4 is 1296x^4-3456x^3y+3456x^2y^2-1536xy^3+256y^4