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## ashleysmith 3 years ago Factor Completely. 81a^2 - 25

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1. Compassionate

(9a - 5)(9a + 5) It is a perfect square binomial.

2. ashleysmith

how did you get that?

3. LifeIsADangerousGame

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)

4. LifeIsADangerousGame

Oops! I'm so sorry, that was a PLUS not a division sign! Here's the correct expression: (9a - 5)(9a + 5)

5. Compassionate

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)

6. ashleysmith

thank you so much <3

7. Compassionate

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.

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