What is expand (A-b)^5 ?

The solution to expand (A-b)^5 is A^5-5A^4b+10A^3b^2-10A^2b^3+5Ab^4-b^5

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Expand Using the Binomial Theorem (A-b)^5

expand

(A - b)^{5}

A^{5} - 5 A^{4} b + 10 A^{3} b^{2} - 10 A^{2} b^{3} + 5 A b^{4} - b^{5}

Solution steps

(A - b)^{5}

Apply binomial theorem:

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

a = A, b = - b

= i = 0 \sum 5 (i 5) A^{(5 - i)} (- b)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} A^{5} (- b)^{0} : A^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} A^{4} (- b)^{1} : - 5 A^{4} b

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} A^{3} (- b)^{2} : 10 A^{3} b^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} A^{2} (- b)^{3} : - 10 A^{2} b^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} A^{1} (- b)^{4} : 5 A b^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} A^{0} (- b)^{5} : - b^{5}

= A^{5} - 5 A^{4} b + 10 A^{3} b^{2} - 10 A^{2} b^{3} + 5 A b^{4} - b^{5}

x^{2} - 7 x - 6

0.1%

0.58%

x, 4 x = 4

- 64

What is expand (A-b)^5 ?
The solution to expand (A-b)^5 is A^5-5A^4b+10A^3b^2-10A^2b^3+5Ab^4-b^5