According to the distributive property which is a way to rewrite the algebraic expression (3x-1)(x-4)

Question

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

Answer 1

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

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

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

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

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

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

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

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

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