Common Factor Pull-Out
Factorisation · Class VIII
For a x + a y, slide a, x, y and see the factored form a (x + y).
- a x + a y15
- a (x + y)15
- Are they equal? (1 yes)1
Formulas in this lab
- a x + a y
- a (x + y)
- Are they equal? (1 yes)
Frequently asked questions
▶What does it mean to take out a common factor?
If two terms share a common factor a, you can write ax + ay = a(x + y). So 6x + 6y = 6(x + y) and 3*4 + 3*5 = 3(4 + 5) = 27. The lab verifies this identity with sliders.
▶How do I use the common factor lab?
Slide a, x and y. The lab shows ax + ay on one side and a(x + y) on the other, confirming they are always equal. Try a = 3, x = 4, y = 5 to see both give 27.
▶How is common factor pull-out used in algebra?
Pulling out the common factor is the first step in solving many algebra problems. For 12x + 18, factor out 6 to get 6(2x + 3). This makes equations and identities easier to handle later. The lab fixes the idea with quick numerical examples.
▶Distributive law vs common factor: same or different?
They are reverses of each other. Distributive law expands a(x + y) into ax + ay. Common factor pull-out collapses ax + ay back into a(x + y). The lab shows both sides match, so you see both views at once.