Question

Factorise:

7xy² – 7x + 2y² – 2

Answer 1

We are given the expression:

7xy² – 7x + 2y² – 2

Step 1: Group the terms

We can start by grouping the terms in pairs:

(7xy² – 7x) + (2y² – 2)

Step 2: Factor each group

Factor out the common factors from each group:

7x(y² – 1) + 2(y² – 1)

Step 3: Factor out the common binomial factor

Now, we can factor out the common binomial factor (y² – 1):

(7x + 2) (y² – 1)

Step 4: Recognize the difference of squares

The expression y² – 1 is a difference of squares, so we can factor it further:

y² – 1 = (y – 1) (y + 1)

Final factorisation:

Thus, the fully factorised form is (7x + 2) (y – 1) (y + 1)