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

The solution to expand (x^2-x+2)^2 is x^4-2x^3+5x^2-4x+4

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

expand

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

x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 4

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

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

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

(\frac{1}{e})^{2} ln (\frac{1}{e})

(\frac{a ^{- 4}}{b ^{- 3}}) (\frac{b ^{- 3}}{a ^{- 4}})

[(sin (x) - cos (x))^{2} - 1] sec (x) csc (x)

\frac{3 x ^{2} - 3}{4 x ^{2} + 4 x}

(3 x)^{5}

What is expand (x^2-x+2)^2 ?
The solution to expand (x^2-x+2)^2 is x^4-2x^3+5x^2-4x+4