How do you factor #5y^2-90#?

1 Answer
Apr 18, 2016

Answer:

#5y^2-90 = 5(y-3sqrt(2))(y+3sqrt(2))#

Explanation:

Separate out the common scalar factor #5#, express as a difference of squares, then use the difference of squares identity:

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

with #a=y# and #b=3sqrt(2)# as follows:

#5y^2-90#

#= 5(y^2-18)#

#= 5(y^2-3^2*2)#

#= 5(y^2-(3sqrt(2))^2)#

#= 5(y-3sqrt(2))(y+3sqrt(2))#