You can put this solution on YOUR website! Factor 16x^2+48xy+36y^2
Factor out a Greatest Common Factor first. The greatest common factor is 4.
4(4x^2+12xy+9y^2)
Now factor the polynomial in the parenthesis.
Look at 4x^2 Break it into factor choices: 1x4 or 2x2
Look at 9y^2 Break it into factor choices: 1x9 or 3x3
Lets first try 2x2 and 3x3 for the factor choices:
(2x 3y)(2x 3y)
There are two x's and 2y's because of the 4x^2 and the 9y^2. Our answer has to equal the middle term 12xy.
Now we multiply to see if we picked the right factors of 4 and 9.
The outer 2x multiplied with the outer 3y equals 6xy. The inner 3y multiplied with the inner 2x equals 6xy. 6xy+6xy=12xy That works.
Now we have to figure out our signs. Since 9y^2 and 12xy are both positive both of our signs have to be positive.
The answer is:
(2x+3y)(2x+3y)
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