What is #(r +2)(r- 5)(r -2)(r+5)#?

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Answer 1 · 2016-05-21T15:57:14

#r^4-29r^2+100#

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

#(r-5)(r+5) = r^2-25#

#(r^2-4)xx(r^2-25)= r^4 -29r^2+100#

Answer 2 · 2016-05-21T16:01:49

We will evaluate this by using difference of squares patterns.

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

Looking closely at this problem, we find there are two differences of squares: #[(r + 2) and (r - 2)]# and #[(r + 5) and (r - 5)]#.

Multiplying, we get:

#= (r + 2)(r - 2)(r + 5)(r - 5)#

#= (r^2 - 4)(r^2 - 25)#

#= r^4- 4r^2 - 25r^2 + 100#

#= r^4 - 29r^2 + 100#

Hopefully this helps!