What is expand (1-x/4)^5 ?

The solution to expand (1-x/4)^5 is 1-(5x)/4+(5x^2)/8-(5x^3)/(32)+(5x^4)/(256)-(x^5)/(1024)

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expand (1-x/4)^5

expand

(1 - \frac{x}{4})^{5}

1 - \frac{5 x}{4} + \frac{5 x ^{2}}{8} - \frac{5 x ^{3}}{32} + \frac{5 x ^{4}}{256} - \frac{x ^{5}}{1024}

Solution steps

(1 - \frac{x}{4})^{5}

Apply binomial theorem:

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

a = 1, b = - \frac{x}{4}

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (- \frac{x}{4})^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (- \frac{x}{4})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} (- \frac{x}{4})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- \frac{x}{4})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- \frac{x}{4})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (- \frac{x}{4})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (- \frac{x}{4})^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (- \frac{x}{4})^{0} : 1

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} (- \frac{x}{4})^{1} : - \frac{5 x}{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- \frac{x}{4})^{2} : \frac{5 x ^{2}}{8}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- \frac{x}{4})^{3} : - \frac{5 x ^{3}}{32}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (- \frac{x}{4})^{4} : \frac{5 x ^{4}}{256}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (- \frac{x}{4})^{5} : - \frac{x ^{5}}{1024}

= 1 - \frac{5 x}{4} + \frac{5 x ^{2}}{8} - \frac{5 x ^{3}}{32} + \frac{5 x ^{4}}{256} - \frac{x ^{5}}{1024}

\frac{d ^{2}}{d x ^{2}} ((y) (5 x^{2} + y^{4} - 21))

94 - 10 cos (\frac{π}{12} (x - 9.3))

A (- 2, - 8) B (2, - 6)

\frac{3 x + 1}{( 2 x + 9 ) ^{2}}

\frac{10}{( q + 4 ) ^{2}}

What is expand (1-x/4)^5 ?
The solution to expand (1-x/4)^5 is 1-(5x)/4+(5x^2)/8-(5x^3)/(32)+(5x^4)/(256)-(x^5)/(1024)