Question

Factorise fully ax + ay + bx + by

Answer 1

We are told to factor the expression ax + ay + bx + by. To factor the given expression, we must use grouping. The first step is to grouping is to 'group' the expression into two different binomials. This results in (ax + ay) + (bx + by). From the first binomial, we can factor out a. From the second, we can factor out b. After doing this, we get a(x + y) + b(x + y). We immediately notice that there are two like terms, (x + y). We can group the two remaining terms together to get (a + b). When we put the two terms together, we get (a + b)(x + y). Therefore, the factored version of ax + ay + bx + by is (a + b)(x + y). Hope this helped!

Answer 2

Ax + ay + bx + by
= (ax + ay) + (bx + by)
Use the Distributive property
a(x + y) + b(x + y)
Use the Distributive property again
(a + b)(x + y)

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