What is expand (x-2+sqrt(2))^2(x-2-sqrt(2))^2 ?

The solution to expand (x-2+sqrt(2))^2(x-2-sqrt(2))^2 is x^4-8x^3+20x^2-16x+4

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expand (x-2+sqrt(2))^2(x-2-sqrt(2))^2

expand

(x - 2 + 2)^{2} (x - 2 - 2)^{2}

x^{4} - 8 x^{3} + 20 x^{2} - 16 x + 4

Solution steps

(x - 2 + 2)^{2} (x - 2 - 2)^{2}

(x - 2 + 2)^{2} = x^{2} + 22 x - 4 x + 6 - 42

= (x^{2} + 22 x - 4 x + 6 - 42) (x - 2 - 2)^{2}

(x - 2 - 2)^{2} = x^{2} - 4 x - 22 x + 6 + 42

= (x^{2} + 22 x - 4 x + 6 - 42) (x^{2} - 4 x - 22 x + 6 + 42)

Distribute parentheses

= x^{2} x^{2} + x^{2} (- 4 x) + x^{2} (- 22 x) + x^{2} \cdot 6 + x^{2} \cdot 42 + 22 x x^{2} + 22 x (- 4 x) + 22 x (- 22 x) + 22 x \cdot 6 + 22 x \cdot 42 + (- 4 x) x^{2} + (- 4 x) (- 4 x) + (- 4 x) (- 22 x) + (- 4 x) \cdot 6 + (- 4 x) \cdot 42 + 6 x^{2} + 6 (- 4 x) + 6 (- 22 x) + 6 \cdot 6 + 6 \cdot 42 + (- 42) x^{2} + (- 42) (- 4 x) + (- 42) (- 22 x) + (- 42) \cdot 6 + (- 42) \cdot 42

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= x^{2} x^{2} - 4 x^{2} x - 22 x^{2} x + 6 x^{2} + 42 x^{2} + 22 x^{2} x - 2 \cdot 42 xx - 2 \cdot 222 xx + 2 \cdot 62 x + 2 \cdot 422 x - 4 x^{2} x + 4 \cdot 4 xx + 4 \cdot 22 xx - 4 \cdot 6 x - 4 \cdot 42 x + 6 x^{2} - 6 \cdot 4 x - 6 \cdot 22 x + 6 \cdot 6 + 6 \cdot 42 - 42 x^{2} + 4 \cdot 42 x + 4 \cdot 222 x - 4 \cdot 62 - 4 \cdot 422

Simplify

x^{2} x^{2} - 4 x^{2} x - 22 x^{2} x + 6 x^{2} + 42 x^{2} + 22 x^{2} x - 2 \cdot 42 xx - 2 \cdot 222 xx + 2 \cdot 62 x + 2 \cdot 422 x - 4 x^{2} x + 4 \cdot 4 xx + 4 \cdot 22 xx - 4 \cdot 6 x - 4 \cdot 42 x + 6 x^{2} - 6 \cdot 4 x - 6 \cdot 22 x + 6 \cdot 6 + 6 \cdot 42 - 42 x^{2} + 4 \cdot 42 x + 4 \cdot 222 x - 4 \cdot 62 - 4 \cdot 422 : x^{4} - 8 x^{3} + 20 x^{2} - 16 x + 4

= x^{4} - 8 x^{3} + 20 x^{2} - 16 x + 4

\frac{d}{d y} ((x (y)) (y^{2} + 1))

\frac{1}{( x - 1 ) ( x - 4 )}

(x - 3) e^{∣ x + 1 ∣}

(t - 2) cos (3 t) e^{2 t}

(\frac{a + x}{1 - a x})^{2}

What is expand (x-2+sqrt(2))^2(x-2-sqrt(2))^2 ?
The solution to expand (x-2+sqrt(2))^2(x-2-sqrt(2))^2 is x^4-8x^3+20x^2-16x+4