Certainly! Let's factorize the expression [tex]\( y p + y t + 2 x p + 2 x t \)[/tex] step by step.
1. Identify and group common terms:
We notice that the expression consists of four terms: [tex]\( y p \)[/tex], [tex]\( y t \)[/tex], [tex]\( 2 x p \)[/tex], and [tex]\( 2 x t \)[/tex].
We can group the terms in a way that highlights common factors:
[tex]\[
(y p + y t) + (2 x p + 2 x t)
\][/tex]
2. Factor out the common factors within each group:
Let's factor out the common factor from each group separately.
- From [tex]\( y p + y t \)[/tex]:
[tex]\[
y p + y t = y(p + t)
\][/tex]
- From [tex]\( 2 x p + 2 x t \)[/tex]:
[tex]\[
2 x p + 2 x t = 2 x (p + t)
\][/tex]
So, the grouped terms now look like:
[tex]\[
y(p + t) + 2 x (p + t)
\][/tex]
3. Factor out the common binomial factor:
We see that both terms share a common factor of [tex]\( (p + t) \)[/tex]. We can factor this out from each term:
[tex]\[
y(p + t) + 2 x (p + t) = (p + t)(y + 2 x)
\][/tex]
4. Write the fully factored form:
The fully factored expression is:
[tex]\[
(p + t)(2 x + y)
\][/tex]
Thus, the expression [tex]\( y p + y t + 2 x p + 2 x t \)[/tex] factors completely to:
[tex]\[
(p + t)(2 x + y)
\][/tex]
