How do you factor #16r^2 - 25a^2 #?

2 Answers
Alan P.
Apr 25, 2018

#16r^2-25a^2=color(blue)((4r+5a)(4r-5a))#

Explanation:

Remember: #(x^2-y^2)# can be factored as #(x+y)(x-y)#

Using #16r^2# as #x^2# (that is using #4r# as #x#), and
using #25a^2# as #y^2# (that is using #5a# as #y#)

we get
#color(white)("XXX")(4r+5a)(4r-5a)#

Jim G.
Apr 25, 2018

#(4r-5a)(4r+5a)#

Explanation:

#16r^2-25a^2" is a "color(blue)"difference of squares"#

#"which factors in general as"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "16r^2=(4r)^2" and "25a^2=(5a)^2#

#rArra=4r" and "b=5a#

#rArr16r^2-25a^2=(4r-5a)(4r+5a)#

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