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Answer 1 · 2018-02-04T13:40:01

#9x^2 + 42xy + 49y^2 - 1#

Instead of triple-foiling and ending up with 9 terms to condense, use this trick:

The first two terms in both polynomials are the same, so you can group them together and treat them as ONE term:

#(3x+7y+1)(3x+7y-1)#

#= ((3x+7y)+1)((3x+7y)-1)#

Now, this is in the form #(a+b)(a-b)#, and we know that:

#(a+b)(a-b) = a^2 - b^2#

Therefore, we can write this expression as:

#= (3x+7y)^2 - 1^2#

To simplify completely, remember the square formula:

#(a+b)^2 = a^2 + 2ab + b^2#

So, we can expand the expression like this:

#((3x)^2 + 2(3x)(7y) + (7y)^2) - 1#

#(9x^2 + 42xy + 49y^2) - 1#

#9x^2 + 42xy + 49y^2 - 1#

Final Answer