Simplify expressions such as 2(x + 3) using the distributive property; no negative numbers | Simplify expressions such as 2(x + 3 + y) using the distributive property; no negative numbers |
Simplify expressions such as −5(2x − 3) using the distributive property | Simplify expressions such as −5(2x − 3 + y) using the distributive property |
Factor expressions such as 2x + 6 using the distributive property; no negative numbers | Factor expressions such as 15x + 30 + 25y using the distributive property; no negative numbers |
Factor linear expressions such as −6x + 3 using the distributive property | Factor linear expressions such as −24x − 8 + 16y using the distributive property |
+ 6) = 2 + 12 + − 5) = 3 + 6 − 15 |
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Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.
The following steps will be useful to factor linear expressions.
Step 1 :
Find the largest common divisor for all the terms in the expression
Step 2 :
Divide each term of the expression by the largest common divisor.
Step 3:
Write the quotients inside the parenthesis.
Step 4 :
Write the largest common divisor and the parenthesis together using multiplication.
Example 1 :
Solution :
Find the largest common divisors for 4x and 8.
The largest common divisor for 4x and 8 is 4.
Divide 4x and 8 by 4
4x/4 = x
8/4 = 2
Write the quotients x and 2 inside the parenthesis and multiply by the largest common divisor 4.
Example 2 :
16a + 64b - 4c
Find the largest common divisors for 16a, 64b and 4c.
The largest common divisor for 16a, 64b and 4c is 4.
Divide 16a, 64b and 4c by 4
16a/4 = 4a
64b/4 = 16b
4c/4 = c
Write the quotients 4a, 16b and c inside the parenthesis and multiply by the largest common divisor 4.
4(4a + 16b - c)
Example 3 :
36x - 16
Find the largest common divisors for 36x and 16.
The largest common divisor for 36x and 16 is 4.
Divide 36x and - 16 by 4.
36x/4 = 9x
-16/4 = -4
Write the quotients 9x and -4 inside the parenthesis and multiply by the largest common divisor 4.
Example 4 :
Find the largest common divisors for 35 and 21a.
The largest common divisor for 35 and 21a is 7.
Divide each term by 7
35/7 = 5
21a/7 = 3a
Write the quotients 5 and 3a inside the parenthesis and multiply by the largest common divisor 7.
35 + 21a = 7(5 + 3a)
Example 5 :
Factor :
4a - 8b + 5ax - 10bx
Since we have four terms, we can group them into two terms
= 4a - 8b + 5ax - 10bx
Common divisor for first two terms, that is 4a and 8b is 4
Common divisor for third and fourth terms, that is 5ax and 10bx is 5x.
Divide first two terms by 4
4a/4 = 1a
- 8b/4 = -2b
Divide third and fourth terms by 5x
5ax/5x = a
-10bx/5x = -2b
= 4(a - 2b) + 5x (a - 2b)
= (a - 2b) (4 + 5x)
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Lesson 8 Problem-Solving Practice Factor Linear Expressions 1. MEASUREMENT A sidewalk has an area that can be represented by the expression (8x + 24) feet. Factor the expression 8x + 24. 2. RENTAL The cost of renting a speedboat can be represented by the expression 50x + 250, where x is the number of hours it is rented. Factor the expression ...
Lesson 8 Homework Practice Factor Linear Expressions Find the GCF of each pair of monomials. 1. 20, 45x 2. 15r, 25 3. 8 ... 10. 50j, 75jk 11. 27cd, 72cde 12. 48t, 60st Factor each expression. If the expression cannot be factored, write cannot be factored. 13. 4x + 12 14. 8r - 14 15. 5x + 35 16. 7 + 14x 17. 32x - 15 18. 24 + 32x 19. 6x - 9 20 ...
Factoring Use the distributive property (open the brackets) Choose the types of problems generated for the worksheet. Choose AT LEAST one type. Type 1: constant times a linear expression with 2 terms, such as 2(x + 6) = 2x + 12 Type 2: constant times a linear expression with more terms, such as 3(y + 2x − 5) = 3y + 6x − 15 Page orientation:
Lesson 5 Homework Practice Factoring Linear Expressions Find the GCF of each pair of monomials. ... 25f, 60g 9. 33c, 55cd 10. 50j, 75jk 11. 27cd, 72cde 12. 48t, 60st Factor each expression. If the expression cannot be factored, write ... The rectangle shown below has a total 24. The Art Club receives $10 plus $2 for area of (4x + 36) square ...
Factoring Linear Expressions: Worksheet Generator. 2/11/2014. Factoring Linear Expressions: Worksheet Generator. Factorize the expressions below. 20x 5. 5(4x 1 ) 20x 4. 3x + 21. 6x + 36.
Course 2 • Chapter 5 Expressions ... Lesson 8 Extra Practice . Factor Linear Expressions . Find the GCF of each pair of monomials. 1. 28, 42. x. 14. 2. 21. a ... 4. 42, 56x y 14 5. 20, 28c cd 4c 6. 5ab, 6b b . 7. 7x, 14xy 7x 8. 14b, 56bc 14b 9. 21a, 63ab21a . Factor each expression. If the expression cannot be factored, write cannot be ...
Factoring Linear Expressions. Give students practice factoring linear expressions with this seventh-grade algebra worksheet! With this worksheet, students will factor linear expressions by finding the greatest common factor and rewriting the expression as a product. The worksheet begins with step-by-step instructions using an example problem ...
Homework: Practice Factoring Linear Expressions Directions: Find the GCF. 1. 24st, 28s 2. 32xyz, 40yz Directions: Factor each expression. If the expression can't be factored, write can't be factored. 3. 12w - 30 12w = 30 = GCF = 12w - 30 = 4. 20 + 5e
Skills Practice Factor Linear Expressions Factor each expression. If the expression cannot be factored, write cannot be factored. 1. 17x + 34 2. 10x + 25 3. 30x + 18 4. 45x - 18 5. 38x - 12 6. 28x + 15 7. 3x - 27 8. 6x + 24 9. 26x - 5 10. 48x + 56
We will be concentrating on linear expressions that have 2 terms (binomial) or 3 terms (trinomial). In both cases, the highest exponent is one. Consider the expression (8 + 12): Numerically speaking: 8 + 12 = 4 ( 2 + 3 ) The greatest common factor of 8 and 12 is 4. The factors of the expression (8 + 12) are 4 and (2 + 3).
Expanding and Factoring Linear Expressions. Worksheet. Give students practice expanding and factoring linear equations with this seventh-grade algebra worksheet! Click the checkbox for the options to print and add to Assignments and Collections.
FACTORING LINEAR EXPRESSIONS. The following steps will be useful to factor linear expressions. Step 1 : Find the largest common divisor for all the terms in the expression. Step 2 : Divide each term of the expression by the largest common divisor. Step 3: Write the quotients inside the parenthesis. Step 4 :
Click here for Answers. . factorisation. Practice Questions. Previous: Trial and Improvement Practice Questions. Next: Decimal and Percentages Practice Questions. The Corbettmaths Practice Questions on Factorisation.
Lesson 8 Factor Linear Expressions A linear expression is in factored form when it is expressed as the product of its factors. Example 1 Factor 5x+ 10. Use the GCF to factor the linear expression. 5x = 5 · x Write the prime factorization of 5x and 10. 10 = 5 · 2 Circle the common factors. The GCF of 5x and 10 is 5. Write each term as a ...
Lesson 6 Homework Practice Add Linear Expressions Add. Use models if needed. 1. (9x + 7) + (x + 3) 2. (-4x + 6) + (x - 5) 3. (-3x + 15) + (-3x + 2) 4. (-2x + 10) + (-8x - 1) 5. ... Write an expression for the total number of cruise ships in the harbor on Monday and Tuesday. b. Write an expression for the total number of cruise ships in the ...
Add Linear Expressions. ... Section 5-8: Factor Linear Expressions. Page 425: Vocabulary Check. Page 426: Key Concept Check. Page 427: Problem Solving. Page 428: Reflect. Exercise 1. Exercise 2. Exercise 3. ... With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence.
Give students more practice breaking down expressions with this seventh-grade algebra worksheet! With this worksheet, students will factor linear expressions by finding the greatest common factor and rewriting the expression as a product. This one-page practice worksheet features 20 expressions with addition and subtraction with two or three terms.
This one-page practice worksheet features 20 expressions with addition and subtraction with two or three terms. If learners need a little more guidance, check out the Factoring Linear Expressions worksheet first for a guided example with practice problems. For even more practice with this important algebra skill, have students complete Practice ...
This is a digital version of my Simplifying and Factoring Expressions Cut and Paste Activity designed in Google Slides.Students will practice simplifying and factoring linear expressions with this Drag & Drop Activity. Students must be able to give the simplified and factored form of a linear expression.
Give students more practice breaking down expressions with this seventh-grade algebra worksheet! Practice Expanding Linear Expressions #1. Worksheet. Students use the distributive property of multiplication to expand linear expressions in this seventh-grade algebra worksheet! Practice Expanding Linear Expressions #2.