16x2 - 25 = (4x + 5) (4x - 5)
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16x2 - 25 = (4x + 5) ( 4x - 5)
16x^2 - 25 Recognise that both 16 and 25 are squared numbers, 16 = 4^(2) & 25 = 5^(2) Substituting 4^(2)x^(2) - 5^(2) = > (4x)^(2) - 5^(2) We now have two squared terms with a negative between them. NB two squared terms with positive does NOT factor. Factoring (4x - 5)(4x + 5)
If you mean 5x^2 -125 then it is 5(x^2 -25) when factored
The difference of two squares is quick way to factor polynomials when certain constraints are met: Namely that you have two squares (e.g. 4, 25, 36x2 , 144a6) and one is subtracting from the others (e.g. 25 - 36x2). IF these two constraints are met, then you are able to factor the polynomial by finding the square roots of the squares. sqrt(25)=5 sqrt(36x2) = 6x Therefore 25 - 36x2 = (5+6x)(5-6x) in factored form. In general, given any two squares, a2 and b2, AND they are subtracting, a2 - b2, you can factor them to be (a + b)(a - b).
n + 25 =====