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What is the relationship between multiplying and factoring

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danielmaduroh
The fundamental idea of multiplying is repeated addition. For example:

[tex]3 \times 5 = 15[/tex]

By taking the number five and add it itself three times we have:

[tex]3 \times 5 = 5+5+5=15[/tex]

In contrast, let's take the number three and add it itself five times, so: 

[tex]3 \times 5 = 3+3+3+3+3=15[/tex].

Both 3 and 5 are called factors that are numbers. We can multiply them to get another number. Multiplying can also be expressed like this:

[tex](a+b)(a-b)[/tex]

So you have the factors:

[tex](a+b) \ and\ (a-b)[/tex] 

You can even write any multiplication as the product of factors. On the other hands, factoring shows that you can write any nth-degree polynomial as the product of linear factors, so:

[tex]f(x)=(x-a)(x-b)(x-c)[/tex]

To conclude the relationship between both concepts is the product of factors.

Answer and explanation;

-When you factor a number, you write it as a product - a list of numbers which, when multiplied, give you the original number.

-Multiplying is making a number bigger by adding itself to itself a certain number of times and factoring is the opposite, taking away a certain number from itself.

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