What is expand (x-y)^4 ?

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

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expand (x-y)^4

expand

(x - y)^{4}

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

Solution steps

(x - y)^{4}

Apply binomial theorem:

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

a = x, b = - y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

f (x) = \frac{x ^{2} - 15 x + 36}{5 x - 60}

x^{2} y + 9 x^{2} y

3 \cdot 3 x

\frac{16 3}{3}

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