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Factorising method

Split into two pairs

ax + ay + bx + by
ax + ay + bx + bya(x + y)b(x + y)shared bracket: (x + y)(a + b)(x + y)

For four terms, group the first two and the last two.

Detailed notes

Worked Example

Factor ax + ay + bx + by by grouping pairs that share common factors.

Step 1: Split the expression into two groups

Group the first two terms and the last two terms.

ax + ay + bx + by = (ax + ay) + (bx + by)

Step 2: Factor each group

Take out a from the first group and b from the second group.

(ax + ay) + (bx + by) = a(x + y) + b(x + y)

Step 3: Notice the repeated bracket

Both parts now contain the same bracket, x + y.

a(x + y) + b(x + y)

Step 4: Factor the repeated bracket

The repeated bracket becomes one factor. The outside terms become the other factor.

ax + ay + bx + by = (a + b)(x + y)