Question

Simplify using the distributive property
7(2z+4)

Answer 1

Use the distributive property to rewrite the expression (x-2)(8x+6)

Answer 2

Simplify the polynomial and type in standard form
(x^2-4x+3)+(2x^2+2x-1)

Answer 3

To simplify \( 7(2z + 4) \) using the distributive property, you multiply \( 7 \) by each term inside the parentheses:

\[
7(2z) + 7(4)
\]

Calculating each part:

\[
7 \cdot 2z = 14z
\]
\[
7 \cdot 4 = 28
\]

Putting it all together, you get:

\[
14z + 28
\]

So, the simplified expression is:

\[
\boxed{14z + 28}
\]

Answer 4

To rewrite the expression \((x - 2)(8x + 6)\) using the distributive property, also known as the FOIL method for binomials, you will multiply each term in the first binomial by each term in the second binomial.

1. **First:** Multiply the first terms:
\[
x \cdot 8x = 8x^2
\]

2. **Outer:** Multiply the outer terms:
\[
x \cdot 6 = 6x
\]

3. **Inner:** Multiply the inner terms:
\[
-2 \cdot 8x = -16x
\]

4. **Last:** Multiply the last terms:
\[
-2 \cdot 6 = -12
\]

Now combine all of these results together:

\[
8x^2 + 6x - 16x - 12
\]

Next, combine the like terms \(6x\) and \(-16x\):

\[
8x^2 + (6x - 16x) - 12 = 8x^2 - 10x - 12
\]

Thus, the expression \((x - 2)(8x + 6)\) rewritten is:

\[
\boxed{8x^2 - 10x - 12}
\]

Answer 5

To simplify the polynomial \((x^2 - 4x + 3) + (2x^2 + 2x - 1)\), you can combine like terms.

1. **Combine the \(x^2\) terms:**
\[
x^2 + 2x^2 = 3x^2
\]

2. **Combine the \(x\) terms:**
\[
-4x + 2x = -2x
\]

3. **Combine the constant terms:**
\[
3 - 1 = 2
\]

Now put it all together:

\[
3x^2 - 2x + 2
\]

Thus, the simplified polynomial in standard form is:

\[
\boxed{3x^2 - 2x + 2}
\]