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

The solution to expand (x-3)(x-4)(x-5)(x+1) is x^4-11x^3+35x^2-13x-60

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

expand

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

x^{4} - 11 x^{3} + 35 x^{2} - 13 x - 60

Solution steps

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

Expand

(x - 3) (x - 4) (x - 5) (x + 1) : (x^{2} - 7 x + 12) (x - 5) (x + 1)

= (x^{2} - 7 x + 12) (x - 5) (x + 1)

Apply FOIL method

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

= (x^{2} - 7 x + 12) (x^{2} - 4 x - 5)

Distribute parentheses

= x^{2} x^{2} + x^{2} (- 4 x) + x^{2} (- 5) - 7 x x^{2} - 7 x (- 4 x) - 7 x (- 5) + 12 x^{2} + 12 (- 4 x) + 12 (- 5)

Simplify

x^{2} x^{2} + x^{2} (- 4 x) + x^{2} (- 5) - 7 x x^{2} - 7 x (- 4 x) - 7 x (- 5) + 12 x^{2} + 12 (- 4 x) + 12 (- 5) : x^{4} - 11 x^{3} + 35 x^{2} - 13 x - 60

= x^{4} - 11 x^{3} + 35 x^{2} - 13 x - 60

- 2 \times (- \frac{3}{2})

2 \times (- 15)

x^{4} - m^{8}

16 i^{3}

- 4 x^{2} + 8 x - 3

What is expand (x-3)(x-4)(x-5)(x+1) ?
The solution to expand (x-3)(x-4)(x-5)(x+1) is x^4-11x^3+35x^2-13x-60