What is expand (x^2-4x+5)^2 ?

The solution to expand (x^2-4x+5)^2 is x^4-8x^3+26x^2-40x+25

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expand (x^2-4x+5)^2

expand

(x^{2} - 4 x + 5)^{2}

x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25

Solution steps

(x^{2} - 4 x + 5)^{2}

Apply exponent rule:

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

(x^{2} - 4 x + 5)^{2} = (x^{2} - 4 x + 5) (x^{2} - 4 x + 5)

= (x^{2} - 4 x + 5) (x^{2} - 4 x + 5)

Distribute parentheses

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

Simplify

x^{2} x^{2} + x^{2} (- 4 x) + x^{2} \cdot 5 - 4 x x^{2} - 4 x (- 4 x) - 4 x \cdot 5 + 5 x^{2} + 5 (- 4 x) + 5 \cdot 5 : x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25

= x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25

\frac{3}{2}

(x^{2} - y^{2})^{3}

(X - 2)^{2}

- \frac{- 6}{2}

\frac{1}{4} \times 5

What is expand (x^2-4x+5)^2 ?
The solution to expand (x^2-4x+5)^2 is x^4-8x^3+26x^2-40x+25