To factorize the given expression [tex]\( yp + yt + 2xp + 2xt \)[/tex], we can follow a systematic approach using common algebraic techniques. Here are the detailed steps:
1. Group the terms:
Let's group the terms in a way that makes it easier to factor common factors.
[tex]\[ y p + y t + 2 x p + 2 x t = (yp + yt) + (2xp + 2xt) \][/tex]
2. Factor out the common factor in each group:
First, consider the group [tex]\( yp + yt \)[/tex]. Notice that [tex]\( y \)[/tex] is common in both terms:
[tex]\[ yp + yt = y(p + t) \][/tex]
Next, consider the group [tex]\( 2xp + 2xt \)[/tex]. Here, [tex]\( 2x \)[/tex] is common in both terms:
[tex]\[ 2xp + 2xt = 2x(p + t) \][/tex]
3. Combine the factored terms:
Now we have:
[tex]\[ y(p + t) + 2x(p + t) \][/tex]
4. Factor out the common binomial factor ([tex]\( p + t \)[/tex]):
Both terms now share a common binomial factor [tex]\( (p + t) \)[/tex]:
[tex]\[ y(p + t) + 2x(p + t) = (p + t)(y + 2x) \][/tex]
Therefore, the completely factored form of the given expression [tex]\( yp + yt + 2xp + 2xt \)[/tex] is:
[tex]\[ (p + t)(2x + y) \][/tex]
This is the fully factorized expression.
