UNIT 6 Factoring and Distributing Expressions _2

UNIT 6 Factoring and Distributing Expressions _2_.pptx

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UNIT 6 Factoring and Distributing Expressions _2_.pptx UNIT 6 Factoring and Distributing Expressions _2_.pptx UNIT 6 Factoring and Distributing Expressions _2_.pptx UNIT 6 Factoring and Distributing Expressions _2_.pptx

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

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
5 + 3 5 + 3
(cost of lunch and snack (cost of lunch and snack
on Monday) 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

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

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?
Now write a new expression to represent the same total.
a b a b

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

7x + 7y = _____________________
15g + 20h = ____________________
18m + 42n = _____________________
30a + 39b = ____________________
55m + 11 = ____________________
7 + 56y = ______________________

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

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

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

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

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

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

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 a b

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

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

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

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

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

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UNIT 6 Factoring and Distributing Expressions _2_.pptx

1. FACTORING EXPRESSIONS Factoring is an important process in algebra which is used to simplify expressions, simplify fractions, and solve equations. 5 5 3 3 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? 2 x 5 2 x 3 (2 times the cost of lunch) (2 times the cost of snack) (2 x 5) + (2 x 3) = 16

2. 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 5 + 3 5 + 3 (cost of lunch and snack (cost of lunch and snack on Monday) on Tuesday) 2 x (5+ 3) = 16

3. 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

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

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

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

7. The Distributive Property

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

9. 7x + 7y = _____________________ 15g + 20h = ____________________ 18m + 42n = _____________________ 30a + 39b = ____________________ 55m + 11 = ____________________ 7 + 56y = ______________________

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

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

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

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

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

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

16. 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 a b

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

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

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

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

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

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