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Chapter 6: Q. 6.83 (page 611)

Factor completely:4p2q-16pq+12q

Short Answer

Expert verified

The required factors are4(p-3)(pq-q)

Step by step solution

01

Step 1. Given Information  

The given expression is4p2q-16pq+12q

02

Step 2. Calculation 

We will factor the expression by taking the common factor outside the paranthesis and then use the middle term splitting method.

4p2q-16pq+12q=4(p2q-4pq+3q)=4(p2q-3pq-pq+3q)=4[pq(p-3)-q(p-3)]=4(p-3)(pq-q)

03

Step 3. Check

We will verify by multiplying the factors.

4(p-3)(pq-q)=4[pq(p-3)-q(p-3)]=4(p2q-3pq-pq+3q)=4(p2q-4pq+3q)=4p2q-16pq+12q

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