SOLUTION: Solve. (7p+6q)to the 2nd power

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Question 112669: Solve.
(7p+6q)to the 2nd power
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%287p%2B6q%29%5E2 Start with the given expression

%287p%2B6q%29%287p%2B6q%29 Expand


Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:%287p%29%2A%287p%29=49p%5E2


Multiply the Outer terms:%287p%29%2A%286q%29=42pq


Multiply the Inner terms:%286q%29%2A%287p%29=42qp


Multiply the Last terms:%286q%29%2A%286q%29=36q%5E2


49p%5E2%2B42pq%2B42qp%2B36q%5E2 Now collect every term to make a single expression



49p%5E2%2B84pq%2B36q%5E2 Now combine like terms





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Answer:
So %287p%2B6q%29%287p%2B6q%29 foils and simplifies to 49p%5E2%2B84pq%2B36q%5E2

In other words, %287p%2B6q%29%287p%2B6q%29=49p%5E2%2B84pq%2B36q%5E2

Notice how 49p%5E2%2B84pq%2B36q%5E2 factors back to the original expression %287p%2B6q%29%287p%2B6q%29 (if you need help with factoring, check out this solver). So this verifies our answer.