What is expand (x^2-6x+9)^2 ?

The solution to expand (x^2-6x+9)^2 is x^4-12x^3+54x^2-108x+81

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expand (x^2-6x+9)^2

expand

(x^{2} - 6 x + 9)^{2}

x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81

Solution steps

(x^{2} - 6 x + 9)^{2}

Apply exponent rule:

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

(x^{2} - 6 x + 9)^{2} = (x^{2} - 6 x + 9) (x^{2} - 6 x + 9)

= (x^{2} - 6 x + 9) (x^{2} - 6 x + 9)

Distribute parentheses

= x^{2} x^{2} + x^{2} (- 6 x) + x^{2} \cdot 9 - 6 x x^{2} - 6 x (- 6 x) - 6 x \cdot 9 + 9 x^{2} + 9 (- 6 x) + 9 \cdot 9

Simplify

x^{2} x^{2} + x^{2} (- 6 x) + x^{2} \cdot 9 - 6 x x^{2} - 6 x (- 6 x) - 6 x \cdot 9 + 9 x^{2} + 9 (- 6 x) + 9 \cdot 9 : x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81

= x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81

\frac{v - 5}{v ^{2} - 10 v + 25}

\frac{2 a x + 4 b x}{3 a y + 6 b y}

\frac{x}{x ^{2} - 1}

\frac{- 8 a ^{2} x ^{3}}{- 8 a ^{2} x ^{3}}

(x + 5)^{3}

What is expand (x^2-6x+9)^2 ?
The solution to expand (x^2-6x+9)^2 is x^4-12x^3+54x^2-108x+81