Multiply
x+2/5x-15 * (10x^2 - 25x - 15)
A. (2x+1)/5(x-3)
B. (2x+1)(x-3)/5
C. (10x+5)(x+2)
D. (x+2)(2x+1)
I get a different answer...pls help? Thx
[ (x+2)/{5(x-3)} ] (5)(2 x^2-5x-3)
[ (x+2)/(x-3)] (2x+1)(x-3)
(x+2)(2x+1)
To multiply the given expression, we can use the distributive property. Let's break it down step by step:
Expression: (x + 2) / (5x - 15) * (10x^2 - 25x - 15)
Step 1: Simplify the first fraction.
(x + 2) / (5x - 15) can be factored as (x + 2) / 5(x - 3).
The expression becomes: (x + 2) / 5(x - 3) * (10x^2 - 25x - 15)
Step 2: Multiply the two polynomials.
To multiply the fractions, we multiply the numerators and denominators separately.
(x + 2) * (10x^2 - 25x - 15) / (5(x - 3))
Step 3: Expand the multiplication.
Using the distributive property, we multiply (x + 2) with each term in (10x^2 - 25x - 15).
(x + 2) * (10x^2 - 25x - 15)
= 10x^3 + 20x^2 - 25x^2 - 50x - 15x - 30
Step 4: Combine like terms.
10x^3 + (20x^2 - 25x^2) - (50x + 15x) - 30
= 10x^3 - 5x^2 - 65x - 30
The final expression is: (10x^3 - 5x^2 - 65x - 30) / (5(x - 3))
Therefore, the answer is not among the options provided.
To multiply the given expression, (x+2)/(5x-15) * (10x^2 - 25x - 15), we can use the distributive property of multiplication over addition/subtraction and then simplify the resulting expression.
Firstly, let's factor out any common terms from both expressions:
10x^2 - 25x - 15 = 5(2x^2 - 5x - 3)
Now, we'll distribute (x+2)/(5x-15) across the factored form of the second expression:
(x+2)/(5x-15) * 5(2x^2 - 5x - 3)
Now let's distribute:
(x+2)/(5x-15) * 5 * 2x^2 - (x+2)/(5x-15) * 5 * 5x - (x+2)/(5x-15) * 5 * 3
Simplifying further, we have:
2(x+2)x^2 - 5(x+2)x - 3(x+2)
Now, we can apply the distributive property again:
2x^3 + 4x^2 - 5x^2 - 10x - 3x - 6
Combining like terms, we get:
2x^3 - x^2 - 13x - 6
Comparing this result with the answer options, it seems that the provided answer choices do not match the result we obtained. Therefore, it seems there may be a mistake in the answer options provided.
However, if you have an alternative answer to the expression, please provide that, and I can help verify it or assist you in finding any potential errors.