What is expand (y-x)^4 ?

The solution to expand (y-x)^4 is y^4-4y^3x+6y^2x^2-4yx^3+x^4

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expand (y-x)^4

expand

(y - x)^{4}

y^{4} - 4 y^{3} x + 6 y^{2} x^{2} - 4 y x^{3} + x^{4}

Solution steps

(y - x)^{4}

Apply binomial theorem:

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

a = y, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= y^{4} - 4 y^{3} x + 6 y^{2} x^{2} - 4 y x^{3} + x^{4}

\frac{2 65}{5}

- 6 x - 5 y - 1 + 8 y^{4} + 10 x^{3} - 5 x^{2}

\frac{4}{5} + \frac{1}{7}

(x^{2})^{- 1} \cdot x^{2}

4 \times 60

What is expand (y-x)^4 ?
The solution to expand (y-x)^4 is y^4-4y^3x+6y^2x^2-4yx^3+x^4