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

The solution to expand (5y-x)^4 is 625y^4-500y^3x+150y^2x^2-20yx^3+x^4

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expand (5y-x)^4

expand

(5 y - x)^{4}

625 y^{4} - 500 y^{3} x + 150 y^{2} x^{2} - 20 y x^{3} + x^{4}

Solution steps

(5 y - x)^{4}

Apply binomial theorem:

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

a = 5 y, b = - x

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 y)^{4} (- x)^{0} : 625 y^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 y)^{3} (- x)^{1} : - 500 y^{3} x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 y)^{2} (- x)^{2} : 150 y^{2} x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 y)^{1} (- x)^{3} : - 20 y x^{3}

Simplify

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

= 625 y^{4} - 500 y^{3} x + 150 y^{2} x^{2} - 20 y x^{3} + x^{4}

5 x \times 4

- 60 \div 20

lo g_{1.2} (2)

3 (x + 2) (x - 3)

\frac{1}{5} \cdot (- 2)

What is expand (5y-x)^4 ?
The solution to expand (5y-x)^4 is 625y^4-500y^3x+150y^2x^2-20yx^3+x^4