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Multiply the polynomials (2r−5)(r+4) .(2 points)

_r2+_ r + _

5 answers

To multiply the polynomials \( (2r - 5)(r + 4) \), we can use the distributive property (also known as the FOIL method for binomials).

  1. Multiply the first terms: \[ 2r \cdot r = 2r^2 \]

  2. Multiply the outer terms: \[ 2r \cdot 4 = 8r \]

  3. Multiply the inner terms: \[ -5 \cdot r = -5r \]

  4. Multiply the last terms: \[ -5 \cdot 4 = -20 \]

Now, we combine all these results together: \[ 2r^2 + 8r - 5r - 20 \]

Combine the like terms \( 8r - 5r \): \[ 2r^2 + 3r - 20 \]

So, the result of multiplying the polynomials is: \[ \boxed{2r^2 + 3r - 20} \]

the answer does not have a - in it, re read the answer thing

I understand that you're looking for a representation without the negative sign in the answer form. Let’s confirm it logically while adjusting the formatting according to your instructions.

After correctly multiplying the polynomials \( (2r - 5)(r + 4) \), we got:

  1. \( 2r \cdot r = 2r^2 \)
  2. \( 2r \cdot 4 = 8r \)
  3. \( -5 \cdot r = -5r \)
  4. \( -5 \cdot 4 = -20 \)

We then combined the results:

\[ 2r^2 + 8r - 5r - 20 \]

This leads to:

\[ 2r^2 + (8r - 5r) - 20 = 2r^2 + 3r - 20 \]

Now you emphasized that the answer should not have a minus in it. We will focus instead just on the structural components, leaving out the context of subtraction:

So arranging it without explicitly showing "minus," we could represent it as:

\( 2r^2 + 3r + (-20) \)

However, keep in mind that \( -20 \) is a necessary part of the polynomial, and every term must reflect the actual output of this multiplication.

In the standard polynomial form, it is:

\[ \boxed{2r^2 + 3r - 20} \]

If you need a specific way to present this, please clarify, and I'd be glad to assist!

the - is a + in the answer

I apologize for any confusion! Let's clarify the process and outcome of the multiplication step by step to ensure we're on the same page.

Given the polynomials \( (2r - 5)(r + 4) \):

  1. Using the distributive property (or FOIL method):
    • First: \( 2r \cdot r = 2r^2 \)
    • Outer: \( 2r \cdot 4 = 8r \)
    • Inner: \( -5 \cdot r = -5r \)
    • Last: \( -5 \cdot 4 = -20 \)

Now, assembling these gives us: \[ 2r^2 + 8r - 5r - 20 \]

Combining like terms: \[ 2r^2 + (8r - 5r) - 20 \] \[ 2r^2 + 3r - 20 \]

If you're looking for an expression without the negative sign for the constant term, we can express it differently, though the mathematical result does indeed contain \( -20 \). However, if you need it presented without a negative sign in writing, based on the context, we can only change the presentation, not the mathematical outcome.

So to answer directly, while respecting all mathematical values, the polynomial is:

\[ \boxed{2r^2 + 3r - 20} \]

If you require a different representation or context, such as adding a positive term in a different format, please guide me, and I’ll assist accordingly!