23 June, 12:22

Find the least common multiple of (2a-1) 2, 1-4a2, and 8a3-12a2+6a-1

0
1. 23 June, 13:57
0
The LCM = - 2 (8a3 - 12a2 + 6a - 1).

Step-by-step explanation:

Least common multiple (LCM) of numbers is list the prime factors of each number, then multiply each factor by the greatest number of times it occurs in all the choosen numbers. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

(2a - 1) 2:

= 2 * (2a - 1).

1 - 4a2:

-1 * (4a2 - 1) = - 1 * (a2 - 1/4).

-1 * (a - 1/2) ^2

= - 1 * (2a - 1) ^2

8a3 - 12a2 + 6a - 1:

Inputting a = 1/2,

1 - 3 + 3 - 1 = 0

So 2a - 1 is a root, dividing its root by the equation,

(2a - 1) (4a2 - 4a + 1)

Inputting 2a - 1 into 4a2 - 4a + 1,

1 - 2 + 1 = 0.

So 2a - 1 is a root, dividing its root by the equation,

(2a - 1) (2a - 1)

Therefore, 8a3 - 12a2 + 6a - 1 = (2a - 1) ^3

The LCM = - 2 (8a3 - 12a2 + 6a - 1)
The text passage contains a mathematical question asking for the least common multiple (LCM) of three algebraic expressions, and it provides a detailed step-by-step solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
23 June, 12:22

Find the least common multiple of (2a-1) 2, 1-4a2, and 8a3-12a2+6a-1

0
1. 23 June, 13:57
0
The LCM = - 2 (8a3 - 12a2 + 6a - 1).

Step-by-step explanation:

Least common multiple (LCM) of numbers is list the prime factors of each number, then multiply each factor by the greatest number of times it occurs in all the choosen numbers. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

(2a - 1) 2:

= 2 * (2a - 1).

1 - 4a2:

-1 * (4a2 - 1) = - 1 * (a2 - 1/4).

-1 * (a - 1/2) ^2

= - 1 * (2a - 1) ^2

8a3 - 12a2 + 6a - 1:

Inputting a = 1/2,

1 - 3 + 3 - 1 = 0

So 2a - 1 is a root, dividing its root by the equation,

(2a - 1) (4a2 - 4a + 1)

Inputting 2a - 1 into 4a2 - 4a + 1,

1 - 2 + 1 = 0.

So 2a - 1 is a root, dividing its root by the equation,

(2a - 1) (2a - 1)

Therefore, 8a3 - 12a2 + 6a - 1 = (2a - 1) ^3

The LCM = - 2 (8a3 - 12a2 + 6a - 1)
user
The text passage contains a mathematical question asking for the least common multiple (LCM) of three algebraic expressions, and it provides a detailed step-by-step solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER