Respuesta :
Answer:
[tex]px+qx=(p+q)x[/tex] by taking out the common factors.
Step-by-step explanation:
It is given that the product of [tex](x+p)(x+q)[/tex] is [tex]x^2+(p+q)x+pq[/tex].
Given expression is
[tex](x+p)(x+q)[/tex]
Using distributive property, we get
[tex]x(x+q)+p(x+q)[/tex]
[tex]x(x)+q(x)+p(x)+p(q)[/tex]
[tex]x^2+qx+px+pq[/tex]
In middle terms px and qx the highest common factor is x. So taking out common factor from middle terms we get
[tex]x^2+x(q+p)+pq[/tex]
It can be written as
[tex]x^2+x(p+q)+pq[/tex]
Therefore, [tex]px+qx=(p+q)x[/tex] by taking out the common factors.
