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(-1)+3x(3x)+x(-4)+x(x)
B)3x^2+x+4
C)3x(x)+3x(14)+-1(-4)
D)3x^2-5x+4

👇

9 answers
(click or scroll down)

👇

Answer 1

Bot GPT 4-o mini answered
2 months ago

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the distributive property, we can distribute each term in the first parentheses by each term in the second parentheses.

Following the distributive property:

1. \(3x \cdot x = 3x^2\)
2. \(3x \cdot (-4) = -12x\)
3. \(-1 \cdot x = -x\)
4. \(-1 \cdot (-4) = 4\)

Now, we combine these results:

- The \(x\) terms: \(-12x - x = -13x\)
- The constant term: \(4\)
- The \(x^2\) term: \(3x^2\)

Putting it all together, we have:

\[
3x^2 - 13x + 4
\]

However, none of the provided options match this result directly. But let's evaluate the options:

A) \(3x(-1) + 3x(3x) + x(-4) + x(x)\) = \( -3x + 9x^2 - 4x + x^2 = 10x^2 - 7x \) (which doesn't match)

B) \(3x^2 + x + 4\) (which doesn't match)

C) \(3x(x) + 3x(14) + -1(-4)\) (which doesn't make sense in context)

D) \(3x^2 - 5x + 4\) (which doesn't match)

There seems to be an error, as none of the options can be reconciled with the correct expression, \(3x^2 - 13x + 4\).

Please verify the options or the problem itself, as none of them accurately represent the expansion of \((3x - 1)(x - 4)\) using the distributive property.

Answer 2

Snow Princess answered
2 months ago

use the distributive property to find which is equivalent to 9x^2 -25

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

Answer 3

Bot GPT 4-o mini answered
2 months ago

To determine which option is equivalent to \(9x^2 - 25\), we can recognize that \(9x^2 - 25\) is a difference of squares. Specifically, it can be factored as follows:

\[
9x^2 - 25 = (3x)^2 - 5^2 = (3x - 5)(3x + 5)
\]

Now let's evaluate the options one by one:

A) \(9x (x-25)\)
This simplifies to \(9x^2 - 225x\), which does not match.

B) \((3x + 5)(3x - 5)\)
This factors correctly back to \(9x^2 - 25\). **This is correct.**

C) \((3x + 5)^2\)
This expands to \(9x^2 + 30x + 25\), which does not match.

D) \((4.5x + 12.5)(4.5x - 12.5)\)
Using the difference of squares:
This expands to \( (4.5x)^2 - (12.5)^2 = 20.25x^2 - 156.25\), which does not match.

Thus, the correct answer among the provided options is:

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

Answer 4

Snow Princess answered
2 months ago

Use the distributive property to verify which is equivalent to (x-5) (x-3)

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

Answer 5

Bot GPT 4-o mini answered
2 months ago

To verify which option is equivalent to \((x - 5)(x - 3)\) using the distributive property, we can expand the expression step by step:

1. Distributing \(x\):
- \(x \cdot x = x^2\)
- \(x \cdot (-3) = -3x\)

2. Distributing \(-5\):
- \(-5 \cdot x = -5x\)
- \(-5 \cdot (-3) = 15\)

Now, combining all these results together gives us:

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

Now that we've expanded \((x - 5)(x - 3)\) as \(x^2 - 8x + 15\), we can now evaluate the options:

A) \(x^2 - 2x + 15\)
- Not a match.

B) \(x^2 - 8x + 15\)
- This is a match! **Correct.**

C) \(2x - 2\)
- Not a match.

D) \(3x^2 - 4x^2 - 3x^2 - 15\)
- Simplifying gives \(-4x^2 - 15\), which is not a match.

Thus, the correct answer among the provided options is:

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

Answer 6

Snow Princess answered
2 months ago

which expression is equivalent to (z+4) (x-4)

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

Answer 7

Bot GPT 4-o mini answered
2 months ago

To find an expression equivalent to \((z + 4)(x - 4)\), we can use the distributive property to expand the expression step by step:

1. Distributing \(z\):
- \(z \cdot x = zx\)
- \(z \cdot (-4) = -4z\)

2. Distributing \(4\):
- \(4 \cdot x = 4x\)
- \(4 \cdot (-4) = -16\)

Combining these results:

\[
(z + 4)(x - 4) = zx - 4z + 4x - 16
\]

Now, let's evaluate the provided options to see which one matches this expression:

A) \(z^2 + 4z(z) - 4(4)\)
This doesn't make sense and doesn't match the form we derived.

B) \(2z^2 - z - 8\)
This doesn't match.

C) \(z^2 - 8z - 16\)
This doesn't match either.

D) \(z^2 + 4z - 4z - 16\)
Here, the \(4z - 4z\) cancels out, simplifying to \(z^2 - 16\), which still doesn't match the derived expression.

None of the provided options match the expanded expression \(zx - 4z + 4x - 16\).
If you meant for \(x\) to be a specific variable or concept in the options, please clarify, or please recheck the options provided, as none appear to be equivalent to \((z + 4)(x - 4)\).

Answer 8

Snow Princess answered
2 months ago

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

A)2x^2+5x+12
B)2x^2 +6x +4
C)x^2 +6x+2
D)2x^2 +3x+2

Answer 9

Bot GPT 4-o mini answered
2 months ago

To simplify the expression \(2(x + 1)(x + 2)\), we can start by expanding the \((x + 1)(x + 2)\) part first using the distributive property (or FOIL method):

1. Multiplying the first terms: \(x \cdot x = x^2\)
2. Multiplying the outer terms: \(x \cdot 2 = 2x\)
3. Multiplying the inner terms: \(1 \cdot x = x\)
4. Multiplying the last terms: \(1 \cdot 2 = 2\)

Combining these results gives us:

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

Now we will multiply the entire result by 2:

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

Thus, \(2(x + 1)(x + 2) = 2x^2 + 6x + 4\).

Now, let's evaluate the options:

A) \(2x^2 + 5x + 12\)
- This does not match.

B) \(2x^2 + 6x + 4\)
- This matches! **Correct.**

C) \(x^2 + 6x + 2\)
- This does not match.

D) \(2x^2 + 3x + 2\)
- This does not match.

Therefore, the correct answer is:

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