What is expand (x^3-3x^2+2x+1)^2 ?

The solution to expand (x^3-3x^2+2x+1)^2 is x^6-6x^5+13x^4-10x^3-2x^2+4x+1

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expand (x^3-3x^2+2x+1)^2

expand

(x^{3} - 3 x^{2} + 2 x + 1)^{2}

x^{6} - 6 x^{5} + 13 x^{4} - 10 x^{3} - 2 x^{2} + 4 x + 1

Solution steps

(x^{3} - 3 x^{2} + 2 x + 1)^{2}

Apply exponent rule:

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

(x^{3} - 3 x^{2} + 2 x + 1)^{2} = (x^{3} - 3 x^{2} + 2 x + 1) (x^{3} - 3 x^{2} + 2 x + 1)

= (x^{3} - 3 x^{2} + 2 x + 1) (x^{3} - 3 x^{2} + 2 x + 1)

Distribute parentheses

= x^{3} x^{3} + x^{3} (- 3 x^{2}) + x^{3} \cdot 2 x + x^{3} \cdot 1 - 3 x^{2} x^{3} - 3 x^{2} (- 3 x^{2}) - 3 x^{2} \cdot 2 x - 3 x^{2} \cdot 1 + 2 x x^{3} + 2 x (- 3 x^{2}) + 2 x \cdot 2 x + 2 x \cdot 1 + 1 \cdot x^{3} + 1 \cdot (- 3 x^{2}) + 1 \cdot 2 x + 1 \cdot 1

Simplify

x^{3} x^{3} + x^{3} (- 3 x^{2}) + x^{3} \cdot 2 x + x^{3} \cdot 1 - 3 x^{2} x^{3} - 3 x^{2} (- 3 x^{2}) - 3 x^{2} \cdot 2 x - 3 x^{2} \cdot 1 + 2 x x^{3} + 2 x (- 3 x^{2}) + 2 x \cdot 2 x + 2 x \cdot 1 + 1 \cdot x^{3} + 1 \cdot (- 3 x^{2}) + 1 \cdot 2 x + 1 \cdot 1 : x^{6} - 6 x^{5} + 13 x^{4} - 10 x^{3} - 2 x^{2} + 4 x + 1

= x^{6} - 6 x^{5} + 13 x^{4} - 10 x^{3} - 2 x^{2} + 4 x + 1

63 x - 9

4 x^{2} + 31 x + 21

\frac{5}{9} - \frac{2}{5}

(3 x y - 1) (4 x y + 2)

\frac{- 2}{12}

What is expand (x^3-3x^2+2x+1)^2 ?
The solution to expand (x^3-3x^2+2x+1)^2 is x^6-6x^5+13x^4-10x^3-2x^2+4x+1