What is expand (a-4)^5 ?

The solution to expand (a-4)^5 is a^5-20a^4+160a^3-640a^2+1280a-1024

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expand (a-4)^5

expand

(a - 4)^{5}

a^{5} - 20 a^{4} + 160 a^{3} - 640 a^{2} + 1280 a - 1024

Solution steps

(a - 4)^{5}

Apply binomial theorem:

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

a = a, b = - 4

= i = 0 \sum 5 (i 5) a^{(5 - i)} (- 4)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} a^{5} (- 4)^{0} : a^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} a^{4} (- 4)^{1} : - 20 a^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} a^{3} (- 4)^{2} : 160 a^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} a^{2} (- 4)^{3} : - 640 a^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} a^{1} (- 4)^{4} : 1280 a

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} a^{0} (- 4)^{5} : - 1024

= a^{5} - 20 a^{4} + 160 a^{3} - 640 a^{2} + 1280 a - 1024

\frac{1000}{100}

32 \times 7

3 \times \frac{2}{9}

\frac{1}{2} \cdot + \frac{4}{3}

\frac{9 ^{3}}{3}

What is expand (a-4)^5 ?
The solution to expand (a-4)^5 is a^5-20a^4+160a^3-640a^2+1280a-1024