Question

What is the relationship between multiplying and factoring

Answer 1

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.

Answer 2

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

$3 \times 5 = 15$

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

$3 \times 5 = 5+5+5=15$

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

$3 \times 5 = 3+3+3+3+3=15$.

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:

$(a+b)(a-b)$

So you have the factors:

$(a+b) \ and\ (a-b)$ 

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:

$f(x)=(x-a)(x-b)(x-c)$

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