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Algebra Calculator

Solve algebra problems step by step

This calculator solves many algebra problems with steps shown. Finds slopes, line equations, completes the square, performs synthetic division, partial fraction decomposition, operations on fractions and polynomials, handles arithmetic/geometric sequences, and many more.
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Permalink: Multiplying Polynomials Calculator

First polynomial:

Second polynomial:

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Solution

Your input: multiply $$$2 x^{2} - 4 x + 2$$$ by $$$2 x^{2} - 4 x + 2$$$.

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:

$$$\left(\color{OrangeRed}{2 x^{2}}\color{Peru}{- 4 x}+\color{Magenta}{2}\right) \cdot \left(\color{Chocolate}{2 x^{2}}\color{DeepPink}{- 4 x}+\color{DarkBlue}{2}\right)=$$$

$$$=\left(\color{OrangeRed}{2 x^{2}}\right)\cdot \left(\color{Chocolate}{2 x^{2}}\right)+\left(\color{OrangeRed}{2 x^{2}}\right)\cdot \left(\color{DeepPink}{- 4 x}\right)+\left(\color{OrangeRed}{2 x^{2}}\right)\cdot \left(\color{DarkBlue}{2}\right)+$$$

$$$+\left(\color{Peru}{- 4 x}\right)\cdot \left(\color{Chocolate}{2 x^{2}}\right)+\left(\color{Peru}{- 4 x}\right)\cdot \left(\color{DeepPink}{- 4 x}\right)+\left(\color{Peru}{- 4 x}\right)\cdot \left(\color{DarkBlue}{2}\right)+$$$

$$$+\left(\color{Magenta}{2}\right)\cdot \left(\color{Chocolate}{2 x^{2}}\right)+\left(\color{Magenta}{2}\right)\cdot \left(\color{DeepPink}{- 4 x}\right)+\left(\color{Magenta}{2}\right)\cdot \left(\color{DarkBlue}{2}\right)=$$$

Simplify the products:

$$$=4 x^{4}- 8 x^{3}+4 x^{2}+$$$

$$$- 8 x^{3}+16 x^{2}- 8 x+$$$

$$$+4 x^{2}- 8 x+4=$$$

Simplify further:

$$$=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$

Answer: $$$\left(2 x^{2} - 4 x + 2\right)\cdot \left(2 x^{2} - 4 x + 2\right)=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$.