Factorization by grouping the terms
Let’s take an algebraic expression xy + y + 2x + 2
Now, grouping the terms as: (xy + y) + (2x + 2)
Taking out y common from the first and 2 from the second group, it may be written as:
xy + y + 2x + 2 = y (x +1) + 2 (x + 1)
xy + y + 2x + 2 = (x + 1) (y + 2)
Thus, the expression turns into a product of two factors.
Example: ax + bx + ay + by
Solution: ax + bx + ay + by = (ax + bx) + (ay + by) [Grouping the terms]
= (a + b)x + (a + b)y
= (a + b) (x + y) [Taking (a + b) common]
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