Which of the following expressions are equivalent to 48a^3-75a? Select all that apply. Answer 1) 3(48a^3-75a). Answer 2) 3a(16a^2-25) Answer 3)3a(4a+5)(4a+5) Answer 4) 3a(4a+5)(4a-5) Answer 5) -3a(25-16a^2) Answer 6) -3a(5-4a)(5+4a)

2 answers
Question:

Which of the following expressions are equivalent to 48a^3-75a? Select all that apply.
Answer 1) 3(48a^3-75a).
Answer 2) 3a(16a^2-25)
Answer 3)3a(4a+5)(4a+5)
Answer 4) 3a(4a+5)(4a-5)
Answer 5) -3a(25-16a^2)
Answer 6) -3a(5-4a)(5+4a)

Answers

Answer:Answer 2) 3a(16a^2-25)Answer 4) 3a(4a+5)(4a-5)Answer 5) -3a(25-16a^2) Answer 6) -3a(5-4a)(5+4a) Step-by-step explanation:The factors of each term are ...2·2·2·2·3·a·a·a3·5·5·aSo, the greatest common factor is 3a. Factoring that out gives ...   3a(16a^2 -25) . . . . . . matches answer 2The factor in parentheses is the difference of squares, so it can be factored. You have memorized the form for the difference of squares ...   p^2 -q^2 = (p -q)(p +q)so you know the factoring of this with p=4a and q=5 will be ...   3a(4a -5)(4a +5) . . . . . . matches answer 4__Any pair of factors can be multiplied by -1 without changing the value of the expression. So, two more answers are equivalent:    (-3a)(-(16a^2 -25) = -3a(25 -16a^2) . . . . . . matches answer 5   (-3a)(-(4a -5)(4a +5) = -3a(5 -4a)(5 +4a) . . . . . . matches answer 6

Answer:2 4 5 6Step-by-step explanation:The highest common factor is 3a That means that 48a^3 must be divided by 3a which means 48a^3 / 3a = 16a^2. Notice what happened. 48/3 = 16. a^3/a = a^2.Now you have to pull out 3a from 75a. That wasn't done to Answer 1. So answer one is incorrect.75a/3a = 25So far what you answer looks like is 3a(16a^2 - 25) which is answer 2===========================================Answer 3 is wrong because one of the factor has to be - 5. Neither one is.===========================================Answer 4 is correct16a^2 - 25 factors into (4a - 5)(4a + 5)So what is written reflects those factors + the 3a==============================================Now we come to the brutal ones. If you take out a minus sign from the brackets, it has the effect of turning the two terms inside the brackets around.-3a(25 - 16a^2) is what the above sentence means. so 5 is correct ==============================================The two terms inside the brackets still factor-3a ( 5 - 4a)(5 + 4a) It is just that they are turned around.6 is correct.===============================================  

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