What is expand (4x-3y)^5 ?

The solution to expand (4x-3y)^5 is 1024x^5-3840x^4y+5760x^3y^2-4320x^2y^3+1620xy^4-243y^5

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expand (4x-3y)^5

expand

(4 x - 3 y)^{5}

1024 x^{5} - 3840 x^{4} y + 5760 x^{3} y^{2} - 4320 x^{2} y^{3} + 1620 x y^{4} - 243 y^{5}

Solution steps

(4 x - 3 y)^{5}

Apply binomial theorem:

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

a = 4 x, b = - 3 y

= i = 0 \sum 5 (i 5) (4 x)^{(5 - i)} (- 3 y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (4 x)^{5} (- 3 y)^{0} : 1024 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} (- 3 y)^{1} : - 3840 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (4 x)^{3} (- 3 y)^{2} : 5760 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (4 x)^{2} (- 3 y)^{3} : - 4320 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (4 x)^{1} (- 3 y)^{4} : 1620 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (4 x)^{0} (- 3 y)^{5} : - 243 y^{5}

= 1024 x^{5} - 3840 x^{4} y + 5760 x^{3} y^{2} - 4320 x^{2} y^{3} + 1620 x y^{4} - 243 y^{5}

(- 2 x^{2})^{3} (4 x^{3})^{- 1}

9 x - 2 + 3 x - 5

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

- ∣ 15 ∣

16 x^{2} - 8 x + 1

What is expand (4x-3y)^5 ?
The solution to expand (4x-3y)^5 is 1024x^5-3840x^4y+5760x^3y^2-4320x^2y^3+1620xy^4-243y^5