What is expand (a-x)^4 ?

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

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expand (a-x)^4

expand

(a - x)^{4}

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

Solution steps

(a - x)^{4}

Apply binomial theorem:

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

a = a, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{6 x}{24 x ^{2} - 216 x}

\frac{6 r}{2 ( r ^{3} ) ^{2}}

45 - 25

6 4^{4}

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

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