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Calcolatrice per il prodotto di polinomi

Moltiplica i polinomi passo dopo passo

La calcolatrice moltiplicherà due polinomi (quadratici, binomi, trinomi, ecc.), mostrando i passaggi.

First polynomial:

Second polynomial:

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Solution

Your input: multiply $$$3 x^{8} - 5 x^{3} - x^{2} + 2 x + 1$$$ by $$$2 x^{2} - 5 x + 3$$$.

To multiply polynomials, multiply each term of the first polynomial by every term of the second polynomial. Then simplify the products and add them. Finally, simplify further if possible.

So, perform the first step:

$$$\left(\color{Violet}{3 x^{8}}\color{Chocolate}{- 5 x^{3}}\color{OrangeRed}{- x^{2}}+\color{Brown}{2 x}+\color{BlueViolet}{1}\right) \cdot \left(\color{Crimson}{2 x^{2}}\color{Red}{- 5 x}+\color{GoldenRod}{3}\right)=$$$

$$$=\left(\color{Violet}{3 x^{8}}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{Violet}{3 x^{8}}\right)\cdot \left(\color{Red}{- 5 x}\right)+\left(\color{Violet}{3 x^{8}}\right)\cdot \left(\color{GoldenRod}{3}\right)+$$$

$$$+\left(\color{Chocolate}{- 5 x^{3}}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{Chocolate}{- 5 x^{3}}\right)\cdot \left(\color{Red}{- 5 x}\right)+\left(\color{Chocolate}{- 5 x^{3}}\right)\cdot \left(\color{GoldenRod}{3}\right)+$$$

$$$+\left(\color{OrangeRed}{- x^{2}}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{OrangeRed}{- x^{2}}\right)\cdot \left(\color{Red}{- 5 x}\right)+\left(\color{OrangeRed}{- x^{2}}\right)\cdot \left(\color{GoldenRod}{3}\right)+$$$

$$$+\left(\color{Brown}{2 x}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{Brown}{2 x}\right)\cdot \left(\color{Red}{- 5 x}\right)+\left(\color{Brown}{2 x}\right)\cdot \left(\color{GoldenRod}{3}\right)+$$$

$$$+\left(\color{BlueViolet}{1}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{BlueViolet}{1}\right)\cdot \left(\color{Red}{- 5 x}\right)+\left(\color{BlueViolet}{1}\right)\cdot \left(\color{GoldenRod}{3}\right)=$$$

Simplify the products:

$$$=6 x^{10}- 15 x^{9}+9 x^{8}+$$$

$$$- 10 x^{5}+25 x^{4}- 15 x^{3}+$$$

$$$- 2 x^{4}+5 x^{3}- 3 x^{2}+$$$

$$$+4 x^{3}- 10 x^{2}+6 x+$$$

$$$+2 x^{2}- 5 x+3=$$$

Simplify further:

$$$=6 x^{10} - 15 x^{9} + 9 x^{8} - 10 x^{5} + 23 x^{4} - 6 x^{3} - 11 x^{2} + x + 3$$$

Answer: $$$\left(3 x^{8} - 5 x^{3} - x^{2} + 2 x + 1\right)\cdot \left(2 x^{2} - 5 x + 3\right)=6 x^{10} - 15 x^{9} + 9 x^{8} - 10 x^{5} + 23 x^{4} - 6 x^{3} - 11 x^{2} + x + 3$$$.