FACTORING EXPRESSIONS Factoring is an important process in

FACTORING EXPRESSIONS Factoring is an important process in algebra which is used to simplify expressions, simplify fractions, and solve equations. Consider the following: Jerry spent $5 for lunch on Monday and again on Tuesday. He spent $3 for snack on each day as well. How much did Jerry spend in all for both days? 5 5 2 x 5 (2 times the cost of lunch) 3 3 2 x 3 (2 times the cost of snack) (2 x 5) + (2 x 3) = 16

Consider the following: Jerry spent $5 for lunch on Monday and again on Tuesday. He spent $3 for snack on each day as well. How much did Jerry spend in all for both days? Does the model shown below represent the situation as well? 5 3 5+3 (cost of lunch and snack on Monday) 5 3 5+3 (cost of lunch and snack on Tuesday) 2 x (5+ 3) = 16

We can look at both expressions to see that they are equivalent. (2 x 5) + (2 x 3) = 2 x (5+ 3) Here’s another view… Let = $1 for lunch Let = $1 for snack

Mathematically, this equation shows an expression that has been “factored. ” (2 x 5) + (2 x 3) = 2 x (5+ 3) GCF times THE OTHER SUM There is a shared factor (GCF) of 2. Take it out and multiply it to the remaining sum. PRACTICE: (5 x 3) + (5 x 4) = ___ x ( __ + __)

WRITE AN EXPRESSION REPRESENTING THE TOTAL. a a _____ b b _____ The expression that represents the total is ______

Can you rearrange the parts of this bar to represent the total in another way? a b Now write a new expression to represent the same total.

The Distributive Property

Use the GCF and the Distributive Property to write equivalent expressions. “Factor. ” 3 g + 3 f = ________ 6 x + 9 y = ________ 3 c + 12 c = ________ 24 b + 8 = _________

Are these expressions equal? How do you know? 6 x + 21 y and 3(2 x + 7 y)

Evaluate each expression to prove that these two expressions are equivalent. Let g = 6 5 g + 7 g g(5 + 7)

Evaluate each expression to prove that these two expressions are equivalent. Let x = 10 14 x + 2 2(7 x + 1)

Fill in the blanks with the numbers that will make the equation true. 4 x + 12 y = ___ (x + 3 y) 35 x + ___y = 5 (7 x + 10 y) ___x + 9 y = 9 (2 x + y) 32 x + 8 y = 8 (___x + y)

Use models to prove that 3(a + b) = 3 a + 3 b

Use the GCF and the Distributive Property to write equivalent expressions in factored form. 4 d + 12 e 18 x + 30 y 21 a + 28 y

Distributing Expressions The expression 2(a + b) tells us that we have 2 of the (a + b)’s. Create a tape diagram representing 2 groups of (a + b). a b

Show your model would look if we grouped together the a’s and then grouped together the b’s. a a b b What expression can we write to represent the new diagram?

Using Area Models to Help Distribute 2 (x + y) x 2 y

Using Area Models to Help Distribute 2 (3 x + 4 y) 3 x 2 4 y

Using Area Models to Help Distribute y (4 x + 5) 4 x y 5

Using Area Models to Help Distribute 3 (7 d + 4 e) 7 d 3 4 e