How do you factor completely #4r^2 -21+5#?

1 Answer
Jun 20, 2016

Answer:

#(2r+4)(2r-4)#

Explanation:

To factor #4r^2-21+5# completely we would begin by combining like terms.

#4r^2-16#

We next would recognize that the binomial is a difference (subtraction) of two squares.

#4r^2 = (2r)(2r)#
and
#16 = (4)(4)#

The difference of two squares always factors in this pattern

#a^2-b^2#

#(a+b)((a-b)#

So our binomial doctors as

#4r^2-16#

#(2r+4)(2r-4)#