What is expand (L-x)^4 ?

The solution to expand (L-x)^4 is L^4-4L^3x+6L^2x^2-4Lx^3+x^4

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expand (L-x)^4

expand

(L - x)^{4}

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

Solution steps

(L - x)^{4}

Apply binomial theorem:

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

a = L, b = - x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{\frac{1}{6}}{\frac{1}{3}}

(a - 4)^{5}

\frac{1000}{100}

32 \times 7

3 \times \frac{2}{9}

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