How do you factor #49x^2 + 64y^2 #?

1 Answer
George C.
Nov 15, 2015

#49x^2+64y^2 = (7x-8iy)(7x+8iy)#

Explanation:

This quadratic has no linear factors with Real coefficients, but it can be treated as a difference of squares using pure imaginary coefficients,

The difference of squares identity can be written:

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

Use this with #a=7x# and #b=8iy# as follows:

#49x^2 + 64y^2 = (7x)^2 + (8y)^2 = (7x)^2 - (8iy)^2#

#= (7x-8iy)(7x+8iy)#

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