Question

Factorise the following:

b(x – y) – 3(y – x) + a(y – x)

Answer 1

b · (x – y) – 3(y – x) + a · (y – x)

Factor out the negative sign from the expression and reorder the terms:

b · (x – y) – 3 · (– (x – y)) + a · (y – x)

Factor out the negative sign from the expression and reorder the terms:

b · (x – y) – 3 · (– (x – y)) + a · (– (x – y))

Multiplying two negatives equals a positive: (–) · (–) = (+)

b · (x – y) + 3(x – y) + a · (– (x – y))

Multiplying a positive and a negative equals a negative: (+) · (–) = (–)

b · (x – y) + 3(x – y) – a · (x – y)

Factor out x – y from the expression:

(x – y) · (b + 3 – a)