Section 2.2.2 Are they Equivalent? Area Models and Equivalent Expressions

What is the rule for each? Warm Up (5 minutes each) What is the rule for each? x f(x) ? 7 5 8 15 9 45 x f(x) ? 11 5 12 15 13 25 You take out a student loan in 2013 for $88512 you plan on paying off 2.5% each subsequent year. What is your remaining balance in 2027? Is this a good strategy?

Equivalent Expressions You will be learning how to use an area model to demonstrate that two expressions are equivalent and new ways to write expressions.

Equivalent Equations Jonah and Graham are working together. Jonah claims that the equation (𝑥+𝑦 ) 2 = 𝑥 2 + 𝑦 2 . Graham thinks that Jonah is wrong. Who is correct? How can you tell? How could (𝑥+𝑦 ) 2 be written correctly?

How can I use an area model? How can an area model help us see the relationship between the expressions 2𝑥−3 2𝑥−3 3𝑥+1 and 6 𝑥 2 −7𝑥−3 ?

Look at the Diagram Below +1 2x -3 3x 6 𝑥 2 -9x How is this diagram used to show that the two expressions are equivalent?

Practice! Use an area model to find the equivalent expression for: (5𝑘−3)(2𝑘−1) 𝑥 2 −3𝑥−4 How does the area model help use the distributive property?

More Practice! Use and area model to show the equivalent expressions for each of the following equations: (3𝑚−5 ) 2 2 𝑥 2 +5𝑥+2 (3𝑥−1)(𝑥+2𝑦−4) 2 𝑥 2 +𝑥−15 𝑥−3 𝑥+3 4 𝑥 2 −49

Special Cases Can the following expressions be represented with an area model? Rewrite each expression. 𝑝(𝑝+3)(2𝑝−1) 𝑥 𝑥+1 +(3𝑥−5)

And yet more practice Refer to #134, on page 99 of your text. Complete each area model and give the two expressions that go with it.

Homework: R & P page 99 problems 135-142