rewrite (2x+9)*(x-3) with the distributive property

Answer 1

To rewrite \((2x + 9)(x - 3)\) using the distributive property, we need to distribute each term in the first parenthesis with each term in the second parenthesis.

1. Distribute \(2x\) to both terms in \((x - 3)\): \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-3) = -6x \]

2. Distribute \(9\) to both terms in \((x - 3)\): \[ 9 \cdot x = 9x \] \[ 9 \cdot (-3) = -27 \]

Now combine all the results: \[ 2x^2 - 6x + 9x - 27 \]

Now, combine like terms: \[ 2x^2 + ( -6x + 9x ) - 27 = 2x^2 + 3x - 27 \]

Therefore, the expression rewritten using the distributive property is: \[ 2x^2 + 3x - 27 \]

Answer 2

is the expression (2x+4)-2+3x equivalent to 5x+2

Answer 3

Let's simplify the expression \((2x + 4) - 2 + 3x\) step by step to see if it is equivalent to \(5x + 2\).

1. Start with the given expression: \[ (2x + 4) - 2 + 3x \]

2. Distribute and combine like terms:

   • First, simplify \(4 - 2\): \[ 2x + 4 - 2 + 3x = 2x + 2 + 3x \]

3. Combine the \(x\) terms: \[ 2x + 3x = 5x \]

4. Now the expression becomes: \[ 5x + 2 \]

Since we have simplified \((2x + 4) - 2 + 3x\) to \(5x + 2\), it is indeed equivalent to \(5x + 2\).

Therefore, the answer is yes, the expressions are equivalent.

Answer 4

is 8+3x equivalent to (8+12x)-9x

Answer 5

To determine if \(8 + 3x\) is equivalent to \((8 + 12x) - 9x\), let's simplify the right side of the equation step by step.

Starting with the expression on the right: \[ (8 + 12x) - 9x \]

1. Distribute and simplify: \[ 8 + 12x - 9x \]

2. Combine like terms: \[ 12x - 9x = 3x \] So, it simplifies to: \[ 8 + 3x \]

Now we see that both expressions are: \[ 8 + 3x \] Thus, we can conclude that:

Yes, \(8 + 3x\) is equivalent to \((8 + 12x) - 9x\).

Answer 6

is (8+21x) equivalent to (8+12x)-9x

Answer 7

To determine if \(8 + 21x\) is equivalent to \((8 + 12x) - 9x\), let's simplify the right side.

Starting with the expression on the right: \[ (8 + 12x) - 9x \]

1. Distribute and simplify: \[ 8 + 12x - 9x \]

2. Combine like terms: \[ 12x - 9x = 3x \] So the expression simplifies to: \[ 8 + 3x \]

Now we compare the simplified expression with \(8 + 21x\): \[ 8 + 3x \quad \text{and} \quad 8 + 21x \]

Since \(3x\) is not equal to \(21x\), we conclude that:

No, \(8 + 21x\) is not equivalent to \((8 + 12x) - 9x\).

Answer 8

identify the coefficients in the expression 8-3y+4+13x

Answer 9

To identify the coefficients in the expression \(8 - 3y + 4 + 13x\), we first rewrite the expression in standard form by arranging the terms properly:

\[ (8 + 4) + 13x - 3y \]

This simplifies to:

\[ 12 + 13x - 3y \]

Now we can identify the coefficients of each variable:

• The coefficient of \(x\) is \(13\).
• The coefficient of \(y\) is \(-3\).
• The constant term (which can also be thought of as the coefficient of \(x^0\) or \(y^0\)) is \(12\).

To summarize, the coefficients are:

• Coefficient of \(x\): \(13\)
• Coefficient of \(y\): \(-3\)
• Constant term: \(12\)