In algebra tiles, what is the relationship between multypling and factoring ?

Question

Algebra types are difficult, what is the difference between when you factor and when you multiply

Answer 1

Constants:   1, 2, 5, 7

Variables:      x, y, h. w

 

Terms:      3x,  8y,  2h        (terms are usually separated by + or -)

                           (note: constants and variables may also be terms)

 

Expressions:   3x+1,  4x +5,  2h + 2w

 

Equations:  x = 4,  y=x+2, P = 2h + 2w

 

A factor is one of the constants or variables that is multiplied with another factor to produce a term.  The term 4x has factors 4 and x.  To factor means to separate what is being multiplied.  So factoring “takes apart” the product of multiplying.

 

Often, to “solve” (that is, to find the value of x, for example) an equation, we must factor a term.

Answer 2

Factoring straddles the line between multiplying and dividing. Let's take a look at the following expression:

3x + 12

Both 3x and 9 have a three in common, so we can factor out that three:

3x ÷ 3 = x

12 ÷ 3 = 4

Now that 3 has been factored out, we set it aside what's left:

3(x + 4)

 

We can get our original expression by distributing (by multiplying) that 3 back in:

x * 3 = 3x

4 * 3 = 12

Giving us:

3x + 12