Factorization - JSS3 Mathematics Past Questions and Answers - page 1

The correct answer is A. 4(𝑥+𝑦).

To factor the expression 4𝑥+4𝑦, we look for the greatest common factor (GCF) of the terms. In this case, the GCF of 4𝑥 and 4𝑦 is 4.

We then factor out the 4 from both terms:

4𝑥+4𝑦 = 4(𝑥+𝑦)

So, the factored form of 4𝑥+4𝑦 is 4(𝑥+𝑦).

To factorize the expression 5𝑚+3𝑛+5𝑛+𝑚𝑛, we first look for common terms that can be grouped together.

Combining the terms with 'm' and those with 'n':

• 5m can be written as 5m
• 3n + 5n = 8n
• mn remains as mn

There does not seem to be any direct way to simplify this so we group the like terms:

5m + mn + 3n + 5n

The expression can be factorized as:

5(𝑚+𝑛)+8𝑛 is incorrect as the m and n are not similar terms. The question can be written as 6m + mn + 8n.

Rearrange the expression to group the similar terms together:

5m + mn + 3n + 5n

This cannot be simplified further as there is no factor for all the terms.

Combine like terms first:

4𝑚+2𝑛+4𝑛+2𝑚𝑛

=4𝑚+6𝑛+2𝑚𝑛

Factor out common factors:

4𝑚+6𝑛+2𝑚𝑛

=2(2𝑚+3𝑛+𝑚𝑛)

Recognize this as a difference of squares:

𝑥2−9𝑦^2

=(𝑥−3𝑦)(𝑥+3𝑦)

This expression is a perfect square trinomial:

𝑎^2+6𝑎𝑏+9𝑏^2

=(𝑎+3𝑏)^2