Question

4x(8 - x)

Answer 1

Multiply the monomial and the polynomial.
3x to the 3rd power(3x + 4)

Answer 2

-5y to the 4th power(6y to the 2nd power + 7y - 2)

Answer 3

(5x - 3)(3x + 2)

Answer 4

what is the perimeter of 5s to the 2nd power + 8s - 12 + 18s to the 2nd power - 3s + 10 + s - 3

Answer 5

To simplify the expression \( 4x(8 - x) \), you can distribute \( 4x \) to both terms in the parentheses:

\[
4x(8) - 4x(x)
\]

This results in:

\[
32x - 4x^2
\]

So, the simplified expression is:

\[
-4x^2 + 32x
\]

Answer 6

To multiply the monomial \( 3x^3 \) by the polynomial \( (3x + 4) \), you will distribute \( 3x^3 \) to each term in the polynomial.

1. Multiply \( 3x^3 \) by \( 3x \):
\[
3x^3 \cdot 3x = 9x^{4}
\]

2. Multiply \( 3x^3 \) by \( 4 \):
\[
3x^3 \cdot 4 = 12x^{3}
\]

Now, combine these results:

\[
9x^{4} + 12x^{3}
\]

So, the result of multiplying the monomial by the polynomial is:

\[
9x^4 + 12x^3
\]

Answer 7

To multiply the monomial \(-5y^4\) by the polynomial \( (6y^2 + 7y - 2) \), you will distribute \(-5y^4\) to each term in the polynomial.

1. Multiply \(-5y^4\) by \(6y^2\):
\[
-5y^4 \cdot 6y^2 = -30y^{6}
\]

2. Multiply \(-5y^4\) by \(7y\):
\[
-5y^4 \cdot 7y = -35y^{5}
\]

3. Multiply \(-5y^4\) by \(-2\):
\[
-5y^4 \cdot -2 = 10y^{4}
\]

Now, combine these results:

\[
-30y^6 - 35y^5 + 10y^4
\]

So, the result of multiplying the monomial by the polynomial is:

\[
-30y^6 - 35y^5 + 10y^4
\]

Answer 8

To multiply the two binomials \( (5x - 3)(3x + 2) \), you can use the distributive property (often called the FOIL method for binomials):

1. **First**: Multiply the first terms in each binomial:
\[
5x \cdot 3x = 15x^2
\]

2. **Outer**: Multiply the outer terms:
\[
5x \cdot 2 = 10x
\]

3. **Inner**: Multiply the inner terms:
\[
-3 \cdot 3x = -9x
\]

4. **Last**: Multiply the last terms:
\[
-3 \cdot 2 = -6
\]

Now, combine all these results:
\[
15x^2 + 10x - 9x - 6
\]

Combine like terms (\(10x - 9x\)):
\[
15x^2 + (10x - 9x) - 6 = 15x^2 + x - 6
\]

So, the result of multiplying the binomials is:

\[
\boxed{15x^2 + x - 6}
\]

Answer 9

To find the perimeter, we first need to simplify the given expression. The expression is:

\[
5s^2 + 8s - 12 + 18s^2 - 3s + 10 + s - 3
\]

We will combine like terms:

1. **Combine the \(s^2\) terms**:
\[
5s^2 + 18s^2 = 23s^2
\]

2. **Combine the \(s\) terms**:
\[
8s - 3s + s = 6s
\]

3. **Combine the constant terms**:
\[
-12 + 10 - 3 = -5
\]

Now, putting it all together, we get:

\[
23s^2 + 6s - 5
\]

If you are referring to "perimeter" in the context of a shape defined by the polynomial, the polynomial may not directly represent a geometric shape with a perimeter. Typically, perimeter Calculation applies to polygons or figures.

However, if you are looking for the expression for the perimeter as a function of \(s\), the result is:

\[
\boxed{23s^2 + 6s - 5}
\]

If you meant something else by "perimeter," please clarify!