Math Lab

Common Factor Pull-Out

Factorisation · Class VIII

For a x + a y, slide a, x, y and see the factored form a (x + y).

3
type a value
112
4
type a value
-1010
5
type a value
-1010
Live values
  • a x + a y15
  • a (x + y)15
  • Are they equal? (1 yes)1
Live readout
a x + a y15
a (x + y)15
Are they equal? (1 yes)1
Common factor a3
x4
y5

Formulas in this lab

  • a x + a y
    ax+aya x + a y
  • a (x + y)
    a(x+y)a(x + y)
  • Are they equal? (1 yes)
    [equal][\text{equal}]
Tip: Pulling out the common factor never changes the value of the expression.

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.