What is expand (x^2-x-1)^2 ?

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

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expand (x^2-x-1)^2

expand

(x^{2} - x - 1)^{2}

x^{4} - 2 x^{3} - x^{2} + 2 x + 1

Solution steps

(x^{2} - x - 1)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x^{2} - x - 1)^{2} = (x^{2} - x - 1) (x^{2} - x - 1)

= (x^{2} - x - 1) (x^{2} - x - 1)

Distribute parentheses

= x^{2} x^{2} + x^{2} (- x) + x^{2} (- 1) - x x^{2} - x (- x) - x (- 1) - 1 \cdot x^{2} - 1 \cdot (- x) - 1 \cdot (- 1)

Simplify

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

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

(3 + i^{3}) (1 - i)

(x + y^{- 1})^{- 1}

3 x y (3 x - y) + 2 (3 x - y)

- (8 a - 6 b - c) + (2 a + 8 b + c)

\frac{z ^{2} z ^{4}}{z ^{3} z ^{- 1}}

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