How do you factor a perfect square trinomial #36b^2 − 24b + 16#?

1 Answer
Tessalsifi · Olivier B.
Jun 12, 2015

We know that #(color(blue)a-color(red)b)²=color(blue)(a^2)-2color(blue)acolor(red)b+color(red)(b²)#

#36b^2=color(blue)((6b)²)=color(blue)(a^2)# ( #color(blue)(a=6b# )
#16=color(red)(4^2)=color(red)(b^2)# ( #color(red)(b=4# )

We are going to check if #-2ab=-24b# :
#-2ab=-2*6b*4=-48b# : incorrect

Thus #36b^2-24b+16# is not a perfect square.

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