Sure, let's factor the given expression step-by-step:
The given expression is:
[tex]\[ 12 + 6y + 2x + xy \][/tex]
To factor this, we will first look for common factors and then group the terms appropriately.
Step 1: Group the expression into pairs to make it easier to factor by grouping.
We can rewrite the expression by grouping:
[tex]\[ (12 + 6y) + (2x + xy) \][/tex]
Step 2: Factor out the greatest common factor (GCF) from each group.
For the first group, [tex]\(12 + 6y\)[/tex]:
- The GCF is 6, so:
[tex]\[ 12 + 6y = 6(2 + y) \][/tex]
For the second group, [tex]\(2x + xy\)[/tex]:
- The GCF is [tex]\(x\)[/tex], so:
[tex]\[ 2x + xy = x(2 + y) \][/tex]
Thus, the expression becomes:
[tex]\[ 6(2 + y) + x(2 + y) \][/tex]
Step 3: Notice that [tex]\(2 + y\)[/tex] is a common factor in both terms. Factor [tex]\(2 + y\)[/tex] out:
[tex]\[ 6(2 + y) + x(2 + y) = (2 + y)(6 + x) \][/tex]
Step 4: Simplify the expression:
We can write it as:
[tex]\[ (x + 6)(y + 2) \][/tex]
Hence, the factored form of the expression [tex]\( 12 + 6y + 2x + xy \)[/tex] is:
[tex]\[ (x + 6)(y + 2) \][/tex]
