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ashleysmith
Factor Completely. 81a^2 - 25
(9a - 5)(9a + 5) It is a perfect square binomial.
how did you get that?
In order to get factors, you have to multiply two expressions with brackets together. So, Compassionate is made the equatoin (9a - 5)(9a - 5) (I don't think there is a such thing as division in this case)
Oops! I'm so sorry, that was a PLUS not a division sign! Here's the correct expression: (9a - 5)(9a + 5)
FACTORING IS THE REVERSE of multiplying. Skill in factoring, then, depends upon skill in multiplying: Lesson 16. As for a quadratic trinomial -- 2x² + 9x − 5 -- it will be factored as a product of binomials: (? ?)(? ?) The first term of each binomial will be the factors of 2x², and the second term will be the factors of 5. Now, how can we produce 2x²? There is only one way: 2x· x : (2x ?)(x ?) And how can we produce 5? Again, there is only one way: 1· 5. But does the 5 go with 2x -- (2x 5)(x 1) or with x -- (2x 1)(x 5) ? Notice: We have not yet placed any signs How shall we decide between these two possibilities? It is the combination that will correctly give the middle term, 9x : 2x² + 9x − 5. Consider the first possibility: (2x 5)(x 1) Is it possible to produce 9x by combining the outers and the inners: 2x (that is, 2x· 1) with 5x ? No, it is not. Therefore, we must eliminate that possibility and consider the other: (2x 1)(x 5) Can we produce 9x by combining 10x with 1x ? Yes -- if we choose +5 and −1: (2x − 1)(x + 5) (2x − 1)(x + 5) = 2x² + 9x − 5. Skill in factoring depends on skill in multiplying -- particularly in picking out the middle term Problem 1. Place the correct signs to give the middle term. a) 2x² + 7x − 15 = (2x − 3)(x + 5) b) 2x² − 7x − 15 = (2x + 3)(x − 5) c) 2x² − x − 15 = (2x + 5)(x − 3) d) 2x² − 13x + 15 = (2x − 3)(x − 5)
thank you so much <3
No problem. You're just putting it in binomials, and if it can factor out again then it's correct! Let me give you can example: 81a^2 - 25 When factored: (9a - 5)(9a + 5) This is true because if I FOIL(First, inner, outer, last.) I will get the original expression: 81a^2 + 45a - 45a - 25 (Notice that my 45a's can be added, but they cancel each other out.) So you're left with (81a^2 - 25) Which is a perfect square binomial.