Factor #(3xx4^x)+ (6xx2^xy) - (45y^2)#?

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Answer 1 · 2018-04-01T19:51:08

Let

#P=3*4^x+6*2^xy-45y^2#

#=3*2^(2x)+6*2^xy-45y^2#

Taking #2^x=a#, we get

#P=3a^2+6ay-45y^2#

#=3(a^2+2ay-15y^2)#

#=3[a^2+5ay-3ay-15y^2]#

#=3[a(a+5y)-3y(a+5y)#

#=3(a+5y)(a-3y)]....where, a=2^x#

#=3(2^x+5y)(2^x-3y)#