What is expand (4x-2y)^5 ?

The solution to expand (4x-2y)^5 is 1024x^5-2560x^4y+2560x^3y^2-1280x^2y^3+320xy^4-32y^5

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expand (4x-2y)^5

expand

(4 x - 2 y)^{5}

1024 x^{5} - 2560 x^{4} y + 2560 x^{3} y^{2} - 1280 x^{2} y^{3} + 320 x y^{4} - 32 y^{5}

Solution steps

(4 x - 2 y)^{5}

Apply binomial theorem:

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

a = 4 x, b = - 2 y

= i = 0 \sum 5 (i 5) (4 x)^{(5 - i)} (- 2 y)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (4 x)^{5} (- 2 y)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} (- 2 y)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (4 x)^{3} (- 2 y)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (4 x)^{2} (- 2 y)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (4 x)^{1} (- 2 y)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (4 x)^{0} (- 2 y)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (4 x)^{5} (- 2 y)^{0} : 1024 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} (- 2 y)^{1} : - 2560 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (4 x)^{3} (- 2 y)^{2} : 2560 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (4 x)^{2} (- 2 y)^{3} : - 1280 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (4 x)^{1} (- 2 y)^{4} : 320 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (4 x)^{0} (- 2 y)^{5} : - 32 y^{5}

= 1024 x^{5} - 2560 x^{4} y + 2560 x^{3} y^{2} - 1280 x^{2} y^{3} + 320 x y^{4} - 32 y^{5}

lo g_{10} (2.2)

- 12 - (- 5)

(2 x + 5) (x + 2)

642

What is expand (4x-2y)^5 ?
The solution to expand (4x-2y)^5 is 1024x^5-2560x^4y+2560x^3y^2-1280x^2y^3+320xy^4-32y^5