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The product of (x+p)(x+q) can be written as x^2+(p+q)x+pq.

An intermediate step in this multiplication is
x^2+px+qx+pq=x^2+(p+q)x+pq.
Explain why px+qx=(p+q)x.
I'm Really confused please help!

1 Answer

6 votes

Answer:


px+qx=(p+q)x by taking out the common factors.

Explanation:

It is given that the product of
(x+p)(x+q) is
x^2+(p+q)x+pq.

Given expression is


(x+p)(x+q)

Using distributive property, we get


x(x+q)+p(x+q)


x(x)+q(x)+p(x)+p(q)


x^2+qx+px+pq

In middle terms px and qx the highest common factor is x. So taking out common factor from middle terms we get


x^2+x(q+p)+pq

It can be written as


x^2+x(p+q)+pq

Therefore,
px+qx=(p+q)x by taking out the common factors.

User Iffat Fatima
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