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Popular >

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

Solution

expand

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

x^{2} x^{2} + x^{2} (- 2 x) + x^{2} \cdot 2 - 2 x x^{2} - 2 x (- 2 x) - 2 x \cdot 2 + 2 x^{2} + 2 (- 2 x) + 2 \cdot 2 : x^{4} - 4 x^{3} + 8 x^{2} - 8 x + 4

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

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Frequently Asked Questions (FAQ)

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