Objectives 1.3

To understand and apply the distributive property

To remove parentheses by multiplying

To insert parentheses by factoring expressions

To perform numerical calculations using the distributive property

To combine like terms to simplify solutions

Think about the different ways to multiply

In your head…

You were probably using the distributive property…

1.3 Investigation 1

Go to page 51 and work on problems 1 to 5…

1.3 Investigation 2

What’s the RULE?

There are different ways to express rules that give the same result.

1.3 Investigation 3

The distributive property allows you to write expressions in different ways…

If you remove the parentheses by multiplying it is called

EXPANDING

If you insert parentheses and take out the GCF it is called

FACTORING

expanding

to

to

factoring

What are factors?

What is a GCF?

Can Variables be factors?

factoring

Look for the GCF, because that is what is being distributed.

4 is the GCF of 4b and 12

So, start by taking out the 4.

4( ? + ? ) = 4b + 12

factor

1.3 Investigation 4

Can the following expression be simplified?

3s + 5p + w + 4s + 4p + 2w

yes, 7s + 9p + 3w

Combining Like Terms

What is a term?

Monomial: is a number or the product of a number and variable(s). x, 2y, ½ xy, 7, and 23x2 are all examples of monomials.The addition or subtraction of monomials

make a polynomial

Like Terms: have exactly the same variables and exponents

Distribute and Combine Like Terms

End of 1.3