Asked by 37432

Multiply the polynomial expression (x + 2)(x - 4)

?x^2 + ?x+ ?

Answers

Answered by 37432
Multiply to simplify the polynomial expression (r - 1)(r^2 - 2r + 3)
?r^3 + ?r^2 + ?r + ?
Answered by 37432
Simplify the polynomial expression (xy - 2)(x² + 1).

?x^3y + ?x² + ?xy + ?
Answered by GPT-4o mini
To multiply the polynomial expression \((x + 2)(x - 4)\), you can use the distributive property (also known as the FOIL method for binomials).

1. First, multiply the first terms:
\[
x \cdot x = x^2
\]

2. Next, multiply the outer terms:
\[
x \cdot (-4) = -4x
\]

3. Then, multiply the inner terms:
\[
2 \cdot x = 2x
\]

4. Finally, multiply the last terms:
\[
2 \cdot (-4) = -8
\]

Now, combine all these results together:
\[
x^2 - 4x + 2x - 8
\]

Combine the like terms \(-4x\) and \(2x\):
\[
x^2 - 2x - 8
\]

Thus, the resulting polynomial expression is:
\[
x^2 - 2x - 8
\]

So, the coefficients for your question are:
- For \(x^2\): \(1\)
- For \(x\): \(-2\)
- For the constant term: \(-8\)

Final answer:
\[
1x^2 + (-2)x + (-8)
\]
Answered by GPT-4o mini
To simplify the polynomial expression \((r - 1)(r^2 - 2r + 3)\), you can apply the distributive property to multiply the binomial by the trinomial.

1. Start by distributing \(r\) to each term in the trinomial:
\[
r \cdot r^2 = r^3
\]
\[
r \cdot (-2r) = -2r^2
\]
\[
r \cdot 3 = 3r
\]

2. Now distribute \(-1\) to each term in the trinomial:
\[
-1 \cdot r^2 = -r^2
\]
\[
-1 \cdot (-2r) = 2r
\]
\[
-1 \cdot 3 = -3
\]

3. Now, combine all the results:
\[
r^3 + (-2r^2) + 3r + (-r^2) + 2r - 3
\]

4. Combine like terms:
- For the \(r^2\) terms: \( -2r^2 - r^2 = -3r^2\)
- For the \(r\) terms: \(3r + 2r = 5r\)

Putting it all together, we have:
\[
r^3 - 3r^2 + 5r - 3
\]

Thus, the simplified expression is:
\[
r^3 - 3r^2 + 5r - 3
\]

So, the coefficients for your question are:
- For \(r^3\): \(1\)
- For \(r^2\): \(-3\)
- For \(r\): \(5\)
- For the constant term: \(-3\)

Final answer:
\[
1r^3 + (-3)r^2 + 5r + (-3)
\]
Answered by GPT-4o mini
To simplify the polynomial expression \((xy - 2)(x^2 + 1)\), we will use the distributive property (also known as the FOIL method for multiplying binomials).

1. Distributing \(xy\) to each term in the second polynomial:
- \(xy \cdot x^2 = x^3y\)
- \(xy \cdot 1 = xy\)

2. Distributing \(-2\) to each term in the second polynomial:
- \(-2 \cdot x^2 = -2x^2\)
- \(-2 \cdot 1 = -2\)

Now, combine all the results:
\[
x^3y + xy - 2x^2 - 2
\]

Next, rearranging the terms to fit the requested format \(?x^3y + ?x^2 + ?xy + ?\):
\[
x^3y - 2x^2 + xy - 2
\]

Thus, the final expression is:
\[
x^3y - 2x^2 + xy - 2
\]

Now, identifying the coefficients:
- For \(x^3y\): \(1\)
- For \(x^2\): \(-2\)
- For \(xy\): \(1\)
- For the constant term: \(-2\)

Final answer:
\[
1x^3y + (-2)x^2 + 1xy + (-2)
\]

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