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(3p + 1)(3p – 1)
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06 Apr 2018, 15:23
06 Apr 2018, 15:23
Expert Reply
00:00
Question Stats:
90% (00:25) correct
9% (00:35) wrong based on 32 sessions
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Quantity A |
Quantity B |
\((3p + 1)(3p - 1)\) |
\(9p^2\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Drill 1
Question: 1
Page: 507
Question: 1
Page: 507
Re: (3p + 1)(3p – 1)
[#permalink]
08 Apr 2018, 01:35
08 Apr 2018, 01:35
1
(a+b)(a-b)=a^2-b^2
(3p + 1)(3p - 1)= 9p^2-1
This is everytime less than 9p^2 as 1 is deducted from it irrespective of it's value. This also hold good even if the number is a fraction or some integer.
(3p + 1)(3p - 1)= 9p^2-1
This is everytime less than 9p^2 as 1 is deducted from it irrespective of it's value. This also hold good even if the number is a fraction or some integer.
Re: (3p + 1)(3p – 1)
[#permalink]
15 Apr 2018, 05:22
15 Apr 2018, 05:22
Expert Reply
Explanation
Evaluate the relationship between the quantities by plugging in values for p: Try p = 2.
Quantity A is 7 × 5 = 35, and Quantity B is 9 × 4 = 36; Quantity B is greater, so eliminate choices (A) and (C). Any value gives the same outcome, so select answer choice (B). Algebraically, you could either FOIL Quantity A or recognize the common quadratics—either way, Quantity A simplifies to 9p2 – 1, which is always exactly 1 less than Quantity B.
Evaluate the relationship between the quantities by plugging in values for p: Try p = 2.
Quantity A is 7 × 5 = 35, and Quantity B is 9 × 4 = 36; Quantity B is greater, so eliminate choices (A) and (C). Any value gives the same outcome, so select answer choice (B). Algebraically, you could either FOIL Quantity A or recognize the common quadratics—either way, Quantity A simplifies to 9p2 – 1, which is always exactly 1 less than Quantity B.
