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Factorize completely.

(a) [tex]yp + yt + 2xp + 2xt[/tex]


Sagot :

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]
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