According to the Distributive Property, which is a way to rewrite the algebraic expression (3x-1)(x-4)?

Question

According to the Distributive Property, which is a way to rewrite the algebraic expression (3x-1)(x-4)?

A. 3x^2-5x+4
B. 3x(x)+3x(-4)+-1(x)+-1(-4)
C. 3x^2+6x+4
D. 3x(-1)+3x(3x)+x(-4)+x(x)

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9 answers
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Answer 1

Bot GPT 4-o mini answered
1 month ago

To rewrite the algebraic expression \((3x-1)(x-4)\) using the Distributive Property, let's apply the FOIL method (First, Outside, Inside, Last):

1. **First:** Multiply the first terms: \(3x \cdot x = 3x^2\)
2. **Outside:** Multiply the outer terms: \(3x \cdot (-4) = -12x\)
3. **Inside:** Multiply the inner terms: \(-1 \cdot x = -1x\)
4. **Last:** Multiply the last terms: \(-1 \cdot (-4) = 4\)

Next, combine all the results:

\[
3x^2 - 12x - 1x + 4 = 3x^2 - 13x + 4
\]

Now, let's evaluate the provided options:

A. \(3x^2 - 5x + 4\) (Incorrect)
B. \(3x(x) + 3x(-4) + -1(x) + -1(-4)\) (This is the correct expansion form)
C. \(3x^2 + 6x + 4\) (Incorrect)
D. \(3x(-1) + 3x(3x) + x(-4) + x(x)\) (Incorrect)

Thus, the correct way to rewrite the expression using the Distributive Property from the choices given is:

**B.** \(3x(x) + 3x(-4) + -1(x) + -1(-4)\)

Answer 2

anonymous answered
1 month ago

Use the Distributive Property to find which expression is equivalent to 9x^2-25.

A. (4.5x+12.5)(4.5x-12.5)
B. 9x(x-25)
C. (3x+5)(3x-5)
D. (3x+5)^2

Answer 3

Bot GPT 4-o mini answered
1 month ago

To find which expression is equivalent to \(9x^2 - 25\), we can recognize that this expression is a difference of squares. The general form for the difference of squares is:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, we can rewrite \(9x^2 - 25\) as:

\[
(3x)^2 - (5)^2
\]

Now, applying the difference of squares formula:

\[
(3x - 5)(3x + 5)
\]

Let's check the answer choices:

A. \((4.5x + 12.5)(4.5x - 12.5)\) (Not correct; not a difference of squares matching the original expression)
B. \(9x(x - 25)\) (This does not represent the original expression)
C. \((3x + 5)(3x - 5)\) (This is correct; it matches our factored form)
D. \((3x + 5)^2\) (This represents a square, not a difference of squares)

The correct answer is:

**C.** \((3x + 5)(3x - 5)\)

Answer 4

anonymous answered
1 month ago

Use the Distributive Property to verify which expression is equivalent to (x-5)(x-3).

A. x^2-8x+15
B. 2x-2
C. 3x^2-4x^2-3x-15
D. x^2-2x + 15

Answer 5

Bot GPT 4-o mini answered
1 month ago

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property (or FOIL method), we'll expand the expression:

Using FOIL:
1. **First:** \(x \cdot x = x^2\)
2. **Outside:** \(x \cdot (-3) = -3x\)
3. **Inside:** \(-5 \cdot x = -5x\)
4. **Last:** \(-5 \cdot (-3) = 15\)

Now, combine all of these results:

\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]

Now let's check the answer choices:

A. \(x^2 - 8x + 15\) (This is correct; it matches our expansion)
B. \(2x - 2\) (This is not correct)
C. \(3x^2 - 4x^2 - 3x - 15\) (This simplifies to \(-x^2 - 3x - 15\), which is not correct)
D. \(x^2 - 2x + 15\) (This is not correct)

The correct answer is:

**A.** \(x^2 - 8x + 15\)

Answer 6

anonymous answered
1 month ago

Which expression is equivalent to (z+4)(z-4)?

A. 2z^2 - z^2 - 8
B. z^2 + 4z - 4z -16
C. z(z) + 4z(z) - 4(4)
D. z^2 - 8z - 16

Answer 7

Bot GPT 4-o mini answered
1 month ago

To find which expression is equivalent to \((z + 4)(z - 4)\), we can recognize that this is a difference of squares, which follows the formula:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, we have:

\[
(z + 4)(z - 4) = z^2 - 4^2 = z^2 - 16
\]

Now, let's evaluate the given options:

A. \(2z^2 - z^2 - 8\)

- This simplifies to \(z^2 - 8\) (Not correct)

B. \(z^2 + 4z - 4z - 16\)

- This simplifies to \(z^2 - 16\) (Correct)

C. \(z(z) + 4z(z) - 4(4)\)

- This would not simplify correctly; it mixes terms incorrectly. We should interpret the expression carefully but it does not match.

D. \(z^2 - 8z - 16\)

- This expression does not match; it includes an extra \(-8z\).

The correct answer is:

**B.** \(z^2 - 16\) (after simplification).

Answer 8

anonymous answered
1 month ago

What is another way to write the expression 2(x+1)(x+2)?

A. 2x^2+3x+2
B. 2x^2+6x+4
C. 2x^2+5x+2
D. x^2+6x+2

Answer 9

Bot GPT 4-o mini answered
1 month ago

To rewrite the expression \(2(x + 1)(x + 2)\), we can first expand the expression inside the parentheses and then distribute \(2\).

1. **Expand \((x + 1)(x + 2)\)** using the distributive property (or FOIL):

- **First:** \(x \cdot x = x^2\)
- **Outside:** \(x \cdot 2 = 2x\)
- **Inside:** \(1 \cdot x = 1x\)
- **Last:** \(1 \cdot 2 = 2\)

Combining these results gives:

\[
x^2 + 2x + 1x + 2 = x^2 + 3x + 2
\]

2. **Now, multiply the entire result by \(2\):**

\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4
\]

Now, let's compare this final expression \(2x^2 + 6x + 4\) against the options given:

A. \(2x^2 + 3x + 2\) (Not correct)

B. \(2x^2 + 6x + 4\) (This is correct)

C. \(2x^2 + 5x + 2\) (Not correct)

D. \(x^2 + 6x + 2\) (Not correct)

Thus, the correct answer is:

**B.** \(2x^2 + 6x + 4\)