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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

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Think about the different ways to multiply In your head… You were probably using the distributive property…

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

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1.3 Investigation 2 What’s the RULE? There are different ways to express rules that give the same result.

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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

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expanding to

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factoring What are factors? What is a GCF? Can Variables be factors?

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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

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factor

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1.3 Investigation 4 Can the following expression be simplified? 3s + 5p + w + 4s + 4p + 2w yes, 7s + 9p + 3w

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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 23x 2 are all examples of monomials. The addition or subtraction of monomials make a polynomial Like Terms : have exactly the same variables and exponents

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Distribute and Combine Like Terms

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End of 1.3

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Do Now: Simplify and write in standard form. 1. -3x 2 - x 2 + 4x – 1 -6x 2. 2 – 7x 3 + 10 – x 3.

Do Now: Simplify and write in standard form. 1. -3x 2 - x 2 + 4x – 1 -6x 2. 2 – 7x 3 + 10 – x 3.

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