Multiply. start fraction k plus 3 over 4 k minus 2 end fraction dot left parenthesis 12 k squared plus 2 k minus 4 right parenthesis
A. Start Fraction 3 left-parenthesis lower k plus 3 right-parenthesis over 3 lower k plus 2 End Fraction
B. Start Fraction 3 left-parenthesis lower k plus 3 right-parenthesis left-parenthesis 2 lower k minus 1 right-parenthesis over 2 End Fraction
C. left-parenthesis k plus 3 right-parenthesis left-parenthesis 3 k plus 2 right-parenthesis
D. left-parenthesis 3 k plus 1 right-parenthesis left-parenthesis 2 k plus 3 right-parenthesis
AAAaannndd the bot gets it wrong yet again!
(k+3)/(4k-2) * (12k^2+2k-4)
= (k+3)/(2(2k-1)) * 2(2k-1)(3k+2)
= (k+3)(3k+2)
So, C
Note: It's always important to check for any potential simplifications before attempting to multiply or factor an expression. In this case, we were able to simplify the expression before multiplying it, which made it easier to solve.
So, why didn't you do it right?
It's just simple algebra!
I apologize for the mistake in my previous response. Thank you for correcting me and showing the correct solution. As an AI language model, I strive to provide the most accurate solutions possible, but I am not perfect and can make mistakes. Once again, I apologize for any confusion that may have caused.
To multiply the given expression, we need to use the distributive property.
First, let's rewrite the expression in factored form:
\( \left( \frac{{k + 3}}{{4k - 2}} \right) \cdot \left( 12k^2 + 2k - 4 \right) \)
Now, we can distribute the fraction over each term in the second expression:
\( \frac{{k + 3}}{{4k - 2}} \cdot 12k^2 + \frac{{k + 3}}{{4k - 2}} \cdot 2k - \frac{{k + 3}}{{4k - 2}} \cdot 4 \)
Simplifying each term:
\( \frac{{12k^2(k + 3)}}{{4k - 2}} + \frac{{2k(k + 3)}}{{4k - 2}} - \frac{{4(k + 3)}}{{4k - 2}} \)
Now, we can simplify each fraction:
\( \frac{{12k^3 + 36k^2}}{{4k - 2}} + \frac{{2k^2 + 6k}}{{4k - 2}} - \frac{{4k + 12}}{{4k - 2}} \)
Next, we can factor out a common factor in each term:
\( \frac{{12k^2(k + 3) + 2k(k + 3) - 4(k + 3)}}{{4k - 2}} \)
Now, we can combine like terms:
\( \frac{{12k^2(k + 3) + 2k(k + 3) - 4(k + 3)}}{{4k - 2}} = \frac{{(12k^2 + 2k - 4)(k + 3)}}{{4k - 2}} \)
Therefore, the correct option is:
C. \( \left( k + 3 \right) \left( 3k + 2 \right) \)
The answer is B.
To solve the problem, we can use the distributive property of multiplication and simplify the expression:
(start fraction k + 3 over 4k - 2 end fraction) (12k² + 2k - 4)
= (k + 3)/4k - 2) (2(6k² + k - 2))
= (k + 3)/(2k - 1) (3k + 2)
= 3(k + 3)(2k - 1)/(2k - 1)
= 3(k + 3)(2k - 1)/(2(k - 1) + 1)
= 3(k + 3)(2k - 1)/(2k - 2 + 1)
= 3(k + 3)(2k - 1)/(2(k - 1) + 1)
= 3(k + 3)(2k - 1)/(2k - 2 + 1)
= 3(k + 3)(2k - 1)/(2k - 1)
= 3(k + 3) (cancel out 2k - 1)
= 3k + 9
Therefore, the answer is B.
Note: It's always important to check for any potential simplifications before attempting to multiply or factor an expression. In this case, we were able to simplify the expression before multiplying it, which made it easier to solve.