How do you factor #49a^2+28ab+4b^2# using the perfect squares formula?

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Answer 1 · 2017-03-16T01:50:37

See the entire solution process below:

The perfect squares formula states:

#x^2 + 2xy + y^2 = (x + y)(x + y)#

For this problem:

If #x^2 = 49a^2# then:

#sqrt(x^2) = +-sqrt(49a^2)#

#x = +-7a#

If #y^2 = 4b^2# then:

#sqrt(y^2) = +-sqrt(4b^2)#

#y = +-2b#

Substituting these into the factors in the formula gives:

#(7a+ 2b)(7a + 2b)#

Or

#(-7a - 2b)(-7a - 2b)#