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

The solution to expand (x^2sqrt(x)-3x+1)^2 is x^5+2x^2sqrt(x)-6x^3sqrt(x)+9x^2-6x+1

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

expand

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

x^{5} + 2 x^{2} x - 6 x^{3} x + 9 x^{2} - 6 x + 1

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

x^{2} x x^{2} x + x^{2} x (- 3 x) + x^{2} x \cdot 1 - 3 x x^{2} x - 3 x (- 3 x) - 3 x \cdot 1 + 1 \cdot x^{2} x + 1 \cdot (- 3 x) + 1 \cdot 1 : x^{5} + 2 x^{2} x - 6 x^{3} x + 9 x^{2} - 6 x + 1

= x^{5} + 2 x^{2} x - 6 x^{3} x + 9 x^{2} - 6 x + 1

(- 3 + i)^{13}

(1 + 2 i)^{4}

\frac{49 7 ( - 7 π + 60 )}{15}

\frac{4 x ( x ^{2} - 28 x - 196 ) ( 7 + x )}{147}

(1 - cos (x) - sin (x))^{2}

What is expand (x^2sqrt(x)-3x+1)^2 ?
The solution to expand (x^2sqrt(x)-3x+1)^2 is x^5+2x^2sqrt(x)-6x^3sqrt(x)+9x^2-6x+1