What is expand (2a-b)^5 ?

The solution to expand (2a-b)^5 is 32a^5-80a^4b+80a^3b^2-40a^2b^3+10ab^4-b^5

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Expand the Trigonometric Expression (2a-b)^5

expand

(2 a - b)^{5}

32 a^{5} - 80 a^{4} b + 80 a^{3} b^{2} - 40 a^{2} b^{3} + 10 a b^{4} - b^{5}

Solution steps

(2 a - b)^{5}

Apply binomial theorem:

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

a = 2 a, b = - b

= i = 0 \sum 5 (i 5) (2 a)^{(5 - i)} (- b)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 a)^{5} (- b)^{0} : 32 a^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 a)^{4} (- b)^{1} : - 80 a^{4} b

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 a)^{3} (- b)^{2} : 80 a^{3} b^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 a)^{2} (- b)^{3} : - 40 a^{2} b^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 a)^{1} (- b)^{4} : 10 a b^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 a)^{0} (- b)^{5} : - b^{5}

= 32 a^{5} - 80 a^{4} b + 80 a^{3} b^{2} - 40 a^{2} b^{3} + 10 a b^{4} - b^{5}

x, 1 0^{x} = 13

x, x^{2} = x

x, 4 x = 36

x, ∣ 3 x - 2 ∣ = 7

t, - 48 t + 2 \leq - 71 t + 14

What is expand (2a-b)^5 ?
The solution to expand (2a-b)^5 is 32a^5-80a^4b+80a^3b^2-40a^2b^3+10ab^4-b^5