Question

Factorize 56x²y - 28xy²:

a) 4xy(14x - 7y)

b) 28xy(2x - y)

c) 56xy(2x - y)

d) 14xy(4x - 2y)

Answer 1

The correct answer is option b) 28xy(2x - y). The expression 56x²y - 28xy² is factorized as 28xy(2x - y), which is option b. The process involves finding the greatest common factor 28xy and dividing each term by it.

Step-by-step explanation:

The correct answer is option b) 28xy(2x - y). To factorize the given expression, 56x²y - 28xy², we look for the greatest common factor (GCF) which in this case is 28xy. We then divide each term by the GCF to find the other factor.

Here's the step-by-step explanation:

1. Identify the GCF of 56x²y and 28xy², which is 28xy.
2. Divide each term by 28xy: (56x²y / 28xy) = 2x, (28xy² / 28xy) = y.
3. Write the original expression as a product of the GCF and the other factors: 28xy(2x - y).

To factorize the expression 56x²y - 28xy², we can factor out the greatest common factor (GCF) of the terms, which is 28xy. This gives us:

28xy(2x - y).

However, we can simplify further by dividing each term by 28 to get:

4xy(14x - 7y).

So, the factorization of 56x²y - 28xy² is 4xy(14x - 7y).