What is expand (x+2)(x+1)(x-2)(x-3) ?

The solution to expand (x+2)(x+1)(x-2)(x-3) is x^4-2x^3-7x^2+8x+12

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expand (x+2)(x+1)(x-2)(x-3)

expand

(x + 2) (x + 1) (x - 2) (x - 3)

x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12

Solution steps

(x + 2) (x + 1) (x - 2) (x - 3)

Expand

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

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

Apply FOIL method

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

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

Distribute parentheses

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

Simplify

x^{3} x + x^{3} (- 3) + x^{2} x + x^{2} (- 3) - 4 xx - 4 x (- 3) - 4 x - 4 (- 3) : x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12

= x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 12

\frac{80}{25}

\frac{80}{27}

60 \times \frac{3}{4}

\frac{80}{40}

14 \times (- 6)

What is expand (x+2)(x+1)(x-2)(x-3) ?
The solution to expand (x+2)(x+1)(x-2)(x-3) is x^4-2x^3-7x^2+8x+12