What is expand (1+x-4x^2)(1+2x+3x^2)(1-2x+4x^2) ?

The solution to expand (1+x-4x^2)(1+2x+3x^2)(1-2x+4x^2) is -48x^6+4x^5+2x^4+5x^3-x^2+x+1

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expand (1+x-4x^2)(1+2x+3x^2)(1-2x+4x^2)

expand

(1 + x - 4 x^{2}) (1 + 2 x + 3 x^{2}) (1 - 2 x + 4 x^{2})

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

Solution steps

(1 + x - 4 x^{2}) (1 + 2 x + 3 x^{2}) (1 - 2 x + 4 x^{2})

Expand

(1 + x - 4 x^{2}) (1 + 2 x + 3 x^{2}) : - 12 x^{4} - 5 x^{3} + x^{2} + 3 x + 1

= (- 12 x^{4} - 5 x^{3} + x^{2} + 3 x + 1) (1 - 2 x + 4 x^{2})

Distribute parentheses

= - 12 x^{4} \cdot 1 - 12 x^{4} (- 2 x) - 12 x^{4} \cdot 4 x^{2} - 5 x^{3} \cdot 1 - 5 x^{3} (- 2 x) - 5 x^{3} \cdot 4 x^{2} + x^{2} \cdot 1 + x^{2} (- 2 x) + x^{2} \cdot 4 x^{2} + 3 x \cdot 1 + 3 x (- 2 x) + 3 x \cdot 4 x^{2} + 1 \cdot 1 + 1 \cdot (- 2 x) + 1 \cdot 4 x^{2}

Simplify

- 12 x^{4} \cdot 1 - 12 x^{4} (- 2 x) - 12 x^{4} \cdot 4 x^{2} - 5 x^{3} \cdot 1 - 5 x^{3} (- 2 x) - 5 x^{3} \cdot 4 x^{2} + x^{2} \cdot 1 + x^{2} (- 2 x) + x^{2} \cdot 4 x^{2} + 3 x \cdot 1 + 3 x (- 2 x) + 3 x \cdot 4 x^{2} + 1 \cdot 1 + 1 \cdot (- 2 x) + 1 \cdot 4 x^{2} : - 48 x^{6} + 4 x^{5} + 2 x^{4} + 5 x^{3} - x^{2} + x + 1

= - 48 x^{6} + 4 x^{5} + 2 x^{4} + 5 x^{3} - x^{2} + x + 1

\frac{x + 4}{x ^{2} - 4} - \frac{x + 1}{x ^{2} - 2 x}

- \frac{4}{7 - 6 i}

\frac{7}{x ^{2} - 5 x - 24} - \frac{2}{x + 3}

(9 x + 5) (- 4 x - 8 + 10 x^{2})

0.1 3^{2}

What is expand (1+x-4x^2)(1+2x+3x^2)(1-2x+4x^2) ?
The solution to expand (1+x-4x^2)(1+2x+3x^2)(1-2x+4x^2) is -48x^6+4x^5+2x^4+5x^3-x^2+x+1