Algebra: Factorisation By Common Factor & Grouping
In this introductory course, you will learn how to simplify algebraic expressions by taking out common factors and using the grouping method. Step by step, you will practice breaking down expressions into simpler parts, making algebra easier to understand and solve.
Related Lessons:
Find HCF Of Algebraic Terms
Before performing factorisation by common factors, you must first find the HCF of the algebraic terms. Work through it systematically, one part at a time:
- Start with the numerical coefficients and find the greatest common number (the HCF of the numbers).
- Next, look at each variable that appears in all the terms.
- For each common variable, choose the smallest power.
- Repeat this process until you have considered all the common variables.
Finally, combine the numerical HCF with the selected variables to form the complete HCF of the expression.
Common Factor Factorisation
To perform Common Factor Factorisation, follow these steps:
- Find the HCF of all the algebraic terms using the method explained earlier.
- Write down the HCF, followed by an open bracket.
- Take the first term of the expression and divide it by the HCF. Write the result inside the bracket.
- Continue dividing each remaining term (second, third, and so on) by the HCF, writing each result inside the bracket.
- After completing all the divisions, close the bracket. The factorisation is now complete.
A common mistake students make is trying to find the terms inside the bracket by using multiplication. Multiplication approach can become confusing, especially with more complex algebraic expressions. Using division is clearer, more systematic, and much more reliable.
5 Examples On Common Factor Factorisation
To further strengthen our concepts, here are additional 5 questions for more practices:
- \(2𝑥𝑦−𝑥𝑦^2+3𝑥^2 𝑦\)
- \(2𝑥^3+10𝑥^3 𝑦−8𝑥^2 𝑦^2\)
- \(4𝜋𝑟^2 ℎ^3+2𝜋𝑟ℎ\)
- \(5𝑎^2 𝑏^2 𝑐−10𝑎𝑏^2 𝑐^3−25𝑎^2 𝑏𝑐\)
- \(\frac{2}{3} 𝑥^2 𝑦^4−\frac{1}{3} 𝑥^3 𝑦−\frac{4}{3} 𝑥^2 𝑦𝑧\)
Answers:
- \(xy\left(2-y+3x\right)\)
- \(2x^2\left(x+5xy-4{y}^2\right)\)
- \(2πr\left(2r{h}^2+1\right)\)
- \(5abc\left(ab-2{\rm{bc}}^2-5a\right)\)
- \(\frac{1}{3}{x}^2y\left(2{y}^3-x-4z\right)\)
Watch Full Concept Breakdown
Factorisation is often easier to understand through video rather than text, as students can clearly see each step of the working process. Below is the complete video explaining the above concepts, carefully broken down into clear, manageable parts for better understanding.