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

Question

?x^2 + ?x+ ?

Answer 1

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: \[ 1x^2 + (-2)x + (-8) \]

Answer 2

Multiply to simplify the polynomial expression (r - 1)(r^2 - 2r + 3)
?r^3 + ?r^2 + ?r + ?

Answer 3

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: \[ 1r^3 + (-3)r^2 + 5r + (-3) \]

Answer 4

Simplify the polynomial expression (xy - 2)(x² + 1).

?x^3y + ?x² + ?xy + ?

Answer 5

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