What is expand (x-1)(x-2)(x-3)(x-4)(x-5) ?

The solution to expand (x-1)(x-2)(x-3)(x-4)(x-5) is x^5-15x^4+85x^3-225x^2+274x-120

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expand (x-1)(x-2)(x-3)(x-4)(x-5)

expand

(x - 1) (x - 2) (x - 3) (x - 4) (x - 5)

x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} + 274 x - 120

Solution steps

(x - 1) (x - 2) (x - 3) (x - 4) (x - 5)

Expand

(x - 1) (x - 2) (x - 3) (x - 4) (x - 5) : (x^{2} - 3 x + 2) (x - 3) (x - 4) (x - 5)

= (x^{2} - 3 x + 2) (x - 3) (x - 4) (x - 5)

Apply FOIL method

(x - 3) (x - 4) : x^{2} - 7 x + 12

= (x^{2} - 3 x + 2) (x^{2} - 7 x + 12) (x - 5)

Expand

(x^{2} - 3 x + 2) (x^{2} - 7 x + 12) : x^{4} - 10 x^{3} + 35 x^{2} - 50 x + 24

= (x^{4} - 10 x^{3} + 35 x^{2} - 50 x + 24) (x - 5)

Distribute parentheses

= x^{4} x + x^{4} (- 5) - 10 x^{3} x - 10 x^{3} (- 5) + 35 x^{2} x + 35 x^{2} (- 5) - 50 xx - 50 x (- 5) + 24 x + 24 (- 5)

Simplify

x^{4} x + x^{4} (- 5) - 10 x^{3} x - 10 x^{3} (- 5) + 35 x^{2} x + 35 x^{2} (- 5) - 50 xx - 50 x (- 5) + 24 x + 24 (- 5) : x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} + 274 x - 120

= x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} + 274 x - 120

\frac{5 3 + 2}{3 + 1}

16 y^{16}

\frac{( n - 2 ) !}{n !}

\frac{( 2 a ^{- 1} b ^{2} ) ^{2}}{( a ^{3} b ) ^{3}}

48 \div 16

What is expand (x-1)(x-2)(x-3)(x-4)(x-5) ?
The solution to expand (x-1)(x-2)(x-3)(x-4)(x-5) is x^5-15x^4+85x^3-225x^2+274x-120