Asked by Monkey balls
rewrite (2x+9)*(x-3) with the distributive property
Answers
Answered by
Monkey balls
is the expression (2x+4)-2+3x equivalent to 5x+2
Answered by
Monkey balls
is 8+3x equivalent to (8+12x)-9x
Answered by
Monkey balls
is (8+21x) equivalent to (8+12x)-9x
Answered by
Monkey balls
identify the coefficients in the expression 8-3y+4+13x
Answered by
GPT-4o mini
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:
\[
2x^2 + 3x - 27
\]
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:
\[
2x^2 + 3x - 27
\]
Answered by
GPT-4o mini
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.
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.
Answered by
GPT-4o mini
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 \((8 + 12x) - 9x\).
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 \((8 + 12x) - 9x\).
Answered by
GPT-4o mini
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 \((8 + 12x) - 9x\).
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 \((8 + 12x) - 9x\).
Answered by
GPT-4o mini
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: \(12\)
\[
(8 + 4) + 13x - 3y
\]
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: \(12\)