Multiply: (K+3)/(4K-2)*(12K^2 + 2k – 4)
• 3(k+3)/(3k+2)
• 3(k+3)(2k-1)/2
• (x-5)(3x+2)
• (x-5)(12x+8)
How?
11
well, 12k^2+2k-4 = 2(3k+2)(2k-1)
so, we have
(k+3)/2(2k-1) * 2(3k+2)(2k-1)
now the 2(2k-1) cancels, leaving
(k+3)(3k+2)
No idea about the 11.
Well, instead of multiplying them out step by step, let's multiply all the things together all at once. That way, we can have a little multiplication party!
So, here we go:
(K+3)/(4K-2) * (12K^2 + 2k – 4)
First, let's distribute (multiply) the numerator (K+3) to all the terms in the second set of parentheses:
(K+3) * 12K^2 + (K+3) * 2k – (K+3) * 4
Next, let's distribute (multiply) the denominator (4K-2) to all the terms in the second set of parentheses:
(4K-2) * 12K^2 + (4K-2) * 2k – (4K-2) * 4
Now, let's simplify:
(K*12K^2 + 3*12K^2) + (K*2k + 3*2k) - (K*4 + 3*4)
(12K^3 + 36K^2) + (2K^2 + 6k) - (4K - 12)
12K^3 + 36K^2 + 2K^2 + 6k - 4K + 12
Finally, let's combine like terms:
12K^3 + (36K^2 + 2K^2) + (-4K) + (6k + 12)
12K^3 + 38K^2 - 4K + 6k + 12
And there you have it! The answer is 12K^3 + 38K^2 - 4K + 6k + 12.
See, math can be hilarious too!
To multiply the given expressions, we can follow the distributive property.
1. Multiply (K+3)/(4K-2) by (12K^2 + 2k – 4):
[(K+3) * (12K^2 + 2K – 4)] / (4K-2)
To simplify, we multiply each term in the numerator by each term in the brackets:
= K * (12K^2 + 2K – 4) + 3 * (12K^2 + 2K – 4) / (4K-2)
= 12K^3 + 2K^2 – 4K + 36K^2 + 6K – 12 / (4K-2)
= 12K^3 + 38K^2 + 2K – 12 / (4K-2)
2. Multiply 3(k+3)/(3k+2) by 3(k+3)(2k-1)/2:
(3(k+3) * 3(k+3)(2k-1)) / (3k + 2) * 2
Apply the distributive property:
= 9(k+3)(2k-1) / (3k + 2) * 2
= [9 * (k+3) * (2k-1)] / (3k + 2) * 2
Simplify:
= 18(k+3)(2k-1) / (3k + 2)
3. Multiply (x-5)(3x+2):
Apply the distributive property:
= x * (3x+2) - 5 * (3x+2)
Simplify:
= 3x^2 + 2x - 15x - 10
= 3x^2 - 13x - 10
4. Multiply (x-5)(12x+8):
Apply the distributive property:
= x * (12x+8) - 5 * (12x+8)
Simplify:
= 12x^2 + 8x - 60x - 40
= 12x^2 - 52x - 40
Hope this helps! If you have any more questions, feel free to ask.
To multiply the given expression (K+3)/(4K-2)*(12K^2 + 2k – 4), you need to use the distributive property of multiplication over addition/subtraction.
Here's the step-by-step process for multiplying the given expression:
1. Start by multiplying each term in the numerator (K+3) by the entire expression in the denominator (12K^2 + 2k – 4).
(K+3) * (12K^2 + 2k – 4)
2. Distribute the multiplication to each term:
(K * 12K^2) + (K * 2k) + (K * -4) + (3 * 12K^2) + (3 * 2k) + (3 * -4)
Simplify the terms:
12K^3 + 2K^2 - 4K + 36K^2 + 6k - 12
3. Combine like terms:
Combine the terms with the same degree of K:
(12K^3) + (2K^2 + 36K^2) + (-4K) + (6k) + (-12)
Simplify the terms:
12K^3 + 38K^2 - 4K + 6k - 12
So, the resulting expression is 12K^3 + 38K^2 - 4K + 6k - 12.
Now, let's check the provided options:
• 3(k+3)/(3k+2):
This option is unrelated to the given expression and does not represent the result of the multiplication.
• 3(k+3)(2k-1)/2:
This option is unrelated to the given expression and does not represent the result of the multiplication.
• (x-5)(3x+2):
This option is unrelated to the given expression and does not represent the result of the multiplication.
• (x-5)(12x+8):
This option is unrelated to the given expression and does not represent the result of the multiplication.
Therefore, none of the provided options matches the result of the given multiplication.