What is expand (x^2-2x+3)^2 ?

The solution to expand (x^2-2x+3)^2 is x^4-4x^3+10x^2-12x+9

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expand (x^2-2x+3)^2

expand

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

x^{4} - 4 x^{3} + 10 x^{2} - 12 x + 9

Solution steps

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

Apply exponent rule:

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

(x^{2} - 2 x + 3)^{2} = (x^{2} - 2 x + 3) (x^{2} - 2 x + 3)

= (x^{2} - 2 x + 3) (x^{2} - 2 x + 3)

Distribute parentheses

= x^{2} x^{2} + x^{2} (- 2 x) + x^{2} \cdot 3 - 2 x x^{2} - 2 x (- 2 x) - 2 x \cdot 3 + 3 x^{2} + 3 (- 2 x) + 3 \cdot 3

Simplify

x^{2} x^{2} + x^{2} (- 2 x) + x^{2} \cdot 3 - 2 x x^{2} - 2 x (- 2 x) - 2 x \cdot 3 + 3 x^{2} + 3 (- 2 x) + 3 \cdot 3 : x^{4} - 4 x^{3} + 10 x^{2} - 12 x + 9

= x^{4} - 4 x^{3} + 10 x^{2} - 12 x + 9

- 11 + (- 15)

8 \cdot 6

\frac{( x + 3 ) ^{3} - 8}{x + 1}

2 4^{4}

(2 a^{2} - a + 4)^{2}

What is expand (x^2-2x+3)^2 ?
The solution to expand (x^2-2x+3)^2 is x^4-4x^3+10x^2-12x+9