Question

Which are equivalent expressions for (4−2z2−z)(3z+5)? Select all that apply.(3 points)6z3−10z2+5z+12z+20−3z26 z cubed minus 10 z squared plus 5 z plus 12 z plus 20 minus 3 z squared−6z3−13z2+7z+20negative 6 z cubed minus 13 z squared plus 7 z plus 20−6z3−7z2−2z+20negative 6 z cubed minus 7 z squared minus 2 z plus 20−6z3−10z2−3z2−5z+12z+20negative 6 z cubed minus 10 z squared minus 3 z squared minus 5 z plus 12 z plus 20−6z3−13z2−5z+12z+20

Answer 1

To determine which of the provided expressions are equivalent to the expression \((4−2z^2−z)(3z+5)\), we first need to fully expand the original expression.

Let's expand \((4 - 2z^2 - z)(3z + 5)\):

1. Distribute \(3z\): \[ 3z(4) + 3z(-2z^2) + 3z(-z) = 12z - 6z^3 - 3z^2 \]

2. Distribute \(5\): \[ 5(4) + 5(-2z^2) + 5(-z) = 20 - 10z^2 - 5z \]

3. Now combine all these results: \[ (12z - 6z^3 - 3z^2) + (20 - 10z^2 - 5z) = -6z^3 + (12z - 5z) + (-3z^2 - 10z^2) + 20 \] \[ = -6z^3 + 7z - 13z^2 + 20 \] Rearranging this, we get: \[ -6z^3 - 13z^2 + 7z + 20 \]

Now, we can compare this final expression with the options provided in your question. We are looking for expressions that match \(-6z^3 - 13z^2 + 7z + 20\).

1. Expression 1: \(6z^3−10z^2+5z+12z+20−3z^2\) simplifies to: \[ 6z^3 − (10z^2 + 3z^2) + (5z + 12z) + 20 = 6z^3 - 13z^2 + 17z + 20 \quad (\text{not equivalent}) \]

2. Expression 2: \(-6z^3−13z^2+7z+20\) matches our result.

3. Expression 3: \(-6z^3−7z^2−2z+20\) does not match the coefficients.

4. Expression 4: \(-6z^3−10z^2−3z^2−5z+12z+20\) simplifies to: \[ -6z^3 − (10z^2 + 3z^2) + (12z - 5z) + 20 = -6z^3 - 13z^2 + 7z + 20 \quad (\text{this is equivalent}) \]

5. Expression 5: \(-6z^3−13z^2−5z+12z+20\) simplifies to: \[ -6z^3 - 13z^2 + (12z - 5z) + 20 = -6z^3 − 13z^2 + 7z + 20 \quad (\text{this is equivalent}) \]

Based on this analysis, the equivalent expressions for \((4−2z^2−z)(3z+5)\) are:

• \(-6z^3−13z^2+7z+20\) (Expression 2)
• \(-6z^3−10z^2−3z^2−5z+12z+20\) (Expression 4)
• \(-6z^3−13z^2−5z+12z+20\) (Expression 5)

Thus, the selected equivalent expressions are Expression 2, Expression 4, and Expression 5.

Answer 2

alright ill let you know if that was correct... i dont alway trust bots

Answer 3

That's completely understandable! It's always good to double-check and verify information, especially when it comes to math or important tasks. If you have any more questions or need further clarification on anything, feel free to ask. I'm here to help!

Answer 4

What is the product of (23g2−6n)2 written in standard form?

Answer 5

To find the product of \((23g^2 - 6n)^2\) and write it in standard form, we will use the formula for the square of a binomial, which states:

\[ (a - b)^2 = a^2 - 2ab + b^2 \]

In this case, let:

• \(a = 23g^2\)
• \(b = 6n\)

Now, applying the formula, we calculate each term:

1. Calculate \(a^2\): \[ (23g^2)^2 = 529g^4 \]

2. Calculate \(2ab\): \[ 2 \cdot (23g^2) \cdot (6n) = 276g^2n \]

3. Calculate \(b^2\): \[ (6n)^2 = 36n^2 \]

Now substituting these values back into the formula gives:

\[ (23g^2 - 6n)^2 = a^2 - 2ab + b^2 = 529g^4 - 276g^2n + 36n^2 \]

Thus, the product \((23g^2 - 6n)^2\) written in standard form is:

\[ \boxed{529g^4 - 276g^2n + 36n^2} \]

Answer 6

bot gpt mini was correct for the first one!! the answers were 2, 4, 5. or B D and E

Answer 7

Great to hear that the answers were correct! I'm glad I could help. If you have any more questions or need assistance with anything else, feel free to reach out. Good luck with your studies!