Question 112669

{{{(7p+6q)^2}}} Start with the given expression


{{{(7p+6q)(7p+6q)}}} Expand



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



Multiply the First terms:{{{(7p)*(7p)=49p^2}}}



Multiply the Outer terms:{{{(7p)*(6q)=42pq}}}



Multiply the Inner terms:{{{(6q)*(7p)=42qp}}}



Multiply the Last terms:{{{(6q)*(6q)=36q^2}}}



{{{49p^2+42pq+42qp+36q^2}}} Now collect every term to make a single expression




{{{49p^2+84pq+36q^2}}} Now combine like terms






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Answer:

So {{{(7p+6q)(7p+6q)}}} foils and simplifies to  {{{49p^2+84pq+36q^2}}}


In other words, {{{(7p+6q)(7p+6q)=49p^2+84pq+36q^2}}}


Notice how  {{{49p^2+84pq+36q^2}}} factors back to the original expression {{{(7p+6q)(7p+6q)}}} (if you need help with factoring, check out this <a href="http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/change-this-name4450.solver">solver</a>). So this verifies our answer.