What is expand (x-a)^4 ?

The solution to expand (x-a)^4 is x^4-4ax^3+6a^2x^2-4a^3x+a^4

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expand (x-a)^4

expand

(x - a)^{4}

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

Solution steps

(x - a)^{4}

Apply binomial theorem:

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

a = x, b = - a

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{3 x - 15}{2 x ^{2} - 50} \cdot \frac{2 x ^{2} + 16 x + 30}{6 x + 9}

1849

\frac{2 15}{3}

(202)^{2}

k (k + 1) (2 k + 1) + 6 (k + 1)^{2}

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