Multiply the polynomial (b+8)(3b−6) to simplify.(1 point)

Question

Responses

3b2+18b−48
3 b squared plus 18 b minus 48

3b2+30b−48
3 b squared plus 30 b minus 48

b2+18b−36
b squared plus 18 b minus 36

b2+30b−48

Answer 1

To multiply the polynomial \((b + 8)(3b - 6)\), we can use the distributive property (also known as the FOIL method for binomials):

1. First: Multiply the first terms: \[ b \cdot 3b = 3b^2 \]

2. Outer: Multiply the outer terms: \[ b \cdot (-6) = -6b \]

3. Inner: Multiply the inner terms: \[ 8 \cdot 3b = 24b \]

4. Last: Multiply the last terms: \[ 8 \cdot (-6) = -48 \]

Next, we combine all the results: \[ 3b^2 - 6b + 24b - 48 \]

Now, combine the like terms \(-6b\) and \(24b\): \[ 3b^2 + 18b - 48 \]

So, the simplified polynomial is: \[ \boxed{3b^2 + 18b - 48} \]

Answer 2

What is the product of the polynomials (x2y+2)(x2−y)?(1 point)
Responses

x4y−x2y2+2x2−2y
x superscript 4 baseline y minus x squared y squared plus 2 x squared minus 2 y

x4y−xy+x2y
x superscript 4 baseline y minus x y plus x squared y

x4y+x2−2y
x superscript 4 baseline y plus x squared minus 2 y

x3y−x2y2+2x2−2y

Answer 3

To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), we will use the distributive property (or FOIL method) to multiply each term in the first polynomial by each term in the second polynomial.

1. Distribute \(x^2y\):

   • \(x^2y \cdot x^2 = x^4y\)
   • \(x^2y \cdot (-y) = -x^2y^2\)

2. Distribute \(2\):

   • \(2 \cdot x^2 = 2x^2\)
   • \(2 \cdot (-y) = -2y\)

Now, we combine all of these results: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

Putting it all together, the final product of the polynomials is: \[ \boxed{x^4y - x^2y^2 + 2x^2 - 2y} \]

Answer 4

Which expression is equivalent to x3(2+y5)?(1 point)
Responses

x3+x3+xy+xy+xy
x cubed plus x cubed plus x y plus x y plus x y

2x3+y5
2 x cubed plus y superscript 5 baseline

x3+2+y5
x cubed plus 2 plus y superscript 5 baseline

2x3+x3y5

Answer 5

To distribute \(x^3\) through the expression \(2 + y^5\), we apply the distributive property.

Starting with \(x^3(2 + y^5)\):

1. Distributing \(x^3\) to \(2\): \[ x^3 \cdot 2 = 2x^3 \]

2. Distributing \(x^3\) to \(y^5\): \[ x^3 \cdot y^5 = x^3y^5 \]

Now combine both results: \[ 2x^3 + x^3y^5 \]

Therefore, the expression equivalent to \(x^3(2 + y^5)\) is: \[ \boxed{2x^3 + x^3y^5} \]