Simplify using the distributive property

Question

7(2z+4)

Answer 1

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 2

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

Answer 3

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 4

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

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:

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