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Popular >

expand (x-5)^4

Solution

expand

(x - 5)^{4}

Solution

x^{4} - 20 x^{3} + 150 x^{2} - 500 x + 625

Solution steps

(x - 5)^{4}

Apply binomial theorem:

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

a = x, b = - 5

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 5)^{1} : - 20 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 5)^{2} : 150 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 5)^{3} : - 500 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 5)^{4} : 625

= x^{4} - 20 x^{3} + 150 x^{2} - 500 x + 625

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Frequently Asked Questions (FAQ)

What is expand (x-5)^4 ?
The solution to expand (x-5)^4 is x^4-20x^3+150x^2-500x+625