Question

Factorise by regrouping and find common factors

12xy -8y + 12 -18x​

Answer 1

Answer:

12xy= 2x2x3multiply by x multiply by y

-8y=-2x2x3xy

12=2x3x3

-18x=-2x3x3

Common factor = 2x3=6

Answer 2

12xy - 8y + 12 - 18x = (3x - 2) (4y - 6)

The common factor is 2.

Step-by-step explanation:

Given, 12xy - 8y + 12 - 18x

= (12xy - 8y) + (12 - 18x)

• Hint: We have regrouped the terms in order to find the common terms for our purpose.

= 4y (3x - 2) + 6 (2 - 3x)

• Hint: The first grouped terms have 4y in common and the second grouped terms have 6 in common.

= 4y (3x - 2) - 6 (3x - 2)

• Hint: We have taken (-) common from the second group and used: (+) (-) = (-).

= (3x - 2) (4y - 6)

• Hint: Since (3x - 2) is the common term, we take that term common and find the required factorization.

Also, 12xy - 8y + 12 - 18x

= 2 (6xy - 4y + 6 - 9x)

• Since each of the terms of the expression has 2 in common, we can take 2 common and conclude that the common factor is 2.

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