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  1. 홈
  2. 계산기
  3. 계산기: 대수학 I
  4. 대수 계산기

다항식 곱셈 계산기

다항식을 단계별로 곱하기

이 계산기는 두 다항식(이차식, 이항식, 삼항식 등)을 곱하고, 단계별 풀이를 보여 줍니다.

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:

$$$\left(\color{Magenta}{3 x^{8}}\color{Fuchsia}{- 5 x^{3}}\color{OrangeRed}{- x^{2}}+\color{DarkBlue}{2 x}+\color{Crimson}{1}\right) \cdot \left(\color{GoldenRod}{2 x^{2}}\color{Chartreuse}{- 5 x}+\color{Red}{3}\right)=$$$

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

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

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

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

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

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