Factoring Algebraic Expressions
Grade 7 Math Worksheets
Any term is formed as a product of factors. For example, in the term 14ab is formed by the factors, 2, 7, a and b.
Similarly, we can factorise an algebraic expression and express it as a product of factors. These factors may be numbers, algebraic expressions or variables.
Schedule a Free session to clear worksheet doubts
No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!
Factoring is the process of writing a polynomial as the product of two or more polynomials.
Example: Factorise 3x + 6
Write each term as a product of irreducible factors:
3x = 3 × x
6 = 2 × 3
3x + 6 = (3 × x) + (2 × 3)
The above two terms have 3 as a common factor.
By distributive property, 3 × (x + 2) = (3 × x) + (2 × 3)
So, 3x + 6 = 3(x + 2), where 3 and (x + 2) are the factors of 3x + 6, and these factors are cannot be reduced further.
Example: Factorise 10xy + 20x
10xy = 2 × 5 × x × y
20x = 2 × 2 × 5 × x
10xy + 20x = (2 × 5 × x × y) + (2 × 2 × 5 × x)
The above two terms have 2 × 5 × x = 10x as the common factor.
By distributive property, 10x × (y + 2) = (2 × 5 × x × y) + (2 × 2 × 5 × x)
So, 10xy + 20x = 10x(y + 2), where 10x and (y + 2) are the factors of 10xy + 20x, and these factors cannot be reduced further.
Check Point
- Factorise 7xy + 49x
- Factorise 12x + 36
- Factorise mn + 10m
- Factorise 24a + 30
- Factorise 11x + 121xy
Answer key
- 7x(y + 7)
- 12(x + 3)
- m(n + 10)
- 6(4a + 5)
- 11x(1 + 11y)
Personalized Online Tutoring from eTutorWorld
eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12, Test Prep help for Standardized tests like SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.
For answers/solutions to any question or to learn concepts, take a FREE TRIAL Session.
No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!
Learn more about Scientific Method and other important topics with 7th Grade Science Tutoring at eTutorWorld. Our expert science tutors break down the topics through interactive one-to-one sessions. We also offer the advantage of customized lesson plans, flexible schedules and convenience of learning from home.
Pricing for Online Tutoring
| Tutoring Package | Validity | Grade (1-12), College |
|---|---|---|
| 5 sessions | 1 Month | $124 |
| 1 session | 1 Month | $25 |
| 10 sessions | 3 months | $239 |
| 15 sessions | 3 months | $354 |
| 20 sessions | 4 months | $449 |
| 50 sessions | 6 months | $1049 |
| 100 sessions | 12 months | $2049 |
