Which of the expressions is equivalent to the expression?
Which of the expressions is equivalent to the expression?
\( 8x^2+4x \)
Which of the expressions is equivalent to the expression?
\( 2a(b+3)+4(b+3) \)
Which of the expressions is equivalent to the expression?
\( 2xy+x^2+3x \)
Which of the expressions is equivalent to the expression?
\( 7z+10b+2bz+35 \)
Which of the expressions is equivalent to the expression?
\( 16-4c \)
Which of the expressions is equivalent to the expression?
Let's solve the problem step by step:
Step 1: Identify the greatest common factor (GCF) of the coefficients in the expression . The numbers are 8 and 4, and the GCF is 4.
Step 2: Factor out the common variable. Both terms have as a common variable factor, so the GCF of the variable part is .
Step 3: Factor the expression using the GCF. We take as a common factor from both terms:
can be rewritten as .
can be rewritten as .
Step 4: Write the factored expression:
.
Step 5: Verify by checking each option. The expression we obtained matches the choice with 2.
Therefore, the equivalent expression is .
Which of the expressions is equivalent to the expression?
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Identify the common factor. The given expression is . Notice that both terms have a common factor, which is .
Step 2: Factor out the common factor. Using the distributive property in reverse, we can factor out :
Step 3: Simplify the expression inside the parentheses if needed. In this case, is already simplified.
Therefore, the expression simplifies to the equivalent expression .
The correct choice that corresponds to this expression is choice 3: .
Which of the expressions is equivalent to the expression?
To solve this problem, we'll follow these steps:
Step 1: Identify the greatest common factor (GCF) in the expression.
Step 2: Factor out the GCF from the expression.
Step 3: Compare the factored expression with the choices provided.
Now, let's work through each step:
Step 1: The expression given is . The GCF of these terms is because it appears in each term.
Step 2: Factor out from each term, which gives: This rewrites the expression in its factored form.
Step 3: Compare the factored form with the answer choices.
Choice 1: does not match the factored form.
Choice 2: exactly matches the factored form.
Choice 3: does not match the factored form.
Choice 4: does not match the factored form.
Therefore, the expression is equivalent to .
Which of the expressions is equivalent to the expression?
To solve this problem, we'll focus on factorization by grouping:
Now, let's work through each step:
Step 1:
Observe that we can reorganize the expression to facilitate grouping:
.
Step 2:
Group into pairs: .
Within each pair, extract common factors:
, noticing that each group factors nicely.
Step 3:
Since both terms now have a common factor of , we can factor it out:
.
Therefore, the expression is equivalent to .
This matches choice 1: .
Which of the expressions is equivalent to the expression?
To solve this problem, we'll follow these steps:
Let's work through each step:
Step 1: Identify the GCF.
The terms in the expression are and . The greatest common factor of and (coefficient of ) is .
Step 2: Factor out the GCF.
Factor out from each term in the expression:
.
Step 3: Compare with the choices.
We factorized to get . Now we compare it with the provided choices:
Therefore, the expression equivalent to is .
Choose the expression that is equivalent to the following:
\( 15z^2+50zx \)
Which expression is equivalent in value to the following:
\( 99ab^2+81b \)
Which of the expressions is equivalent to the expression?
\( 6mn+\frac{3n}{m}+9n^2 \)
Which of the expressions are equal to the expression?
\( 2ab-4bc \)
\( 2b(a-2c) \)
\( 2b(-2c+a) \)
\( 2(-2bc+ab) \)
\( 2a(2bc-b) \)
Which of the expressions are equal to the expression?
\( 12n+48-36mn-144m \)
\( 12(1-3m)(n+4) \)
\( 3(4-12m)(n+4) \)
\( 12(-3m+4)(n+1) \)
\( 12(n+4)-3m(12n+48) \)
Choose the expression that is equivalent to the following:
To solve the problem, the goal is to factor the expression by finding the greatest common factor.
Step 1: Identify the greatest common factor (GCF):
Step 2: Factor the expression using the GCF:
Therefore, the expression is equivalent to .
Which expression is equivalent in value to the following:
To solve this problem, we'll follow these steps:
Step 1: Identify the greatest common factor (GCF) of the coefficients in the expression.
Step 2: Factor out the GCF from the entire expression.
Step 3: Confirm that the factored expression matches one of the given answer choices.
Now, let's work through each step:
Step 1: The coefficients of the terms and are 99 and 81, respectively. The greatest common factor of these coefficients is 9.
Step 2: Both terms, and , contain the variable . We can factor out as well. Thus, the GCF of both terms in the expression is .
Step 3: Factor out of both terms:
Therefore, the equivalent expression to the given algebraic expression is . This matches choice 2.
Thus, the solution to the problem is .
Which of the expressions is equivalent to the expression?
To solve the problem, we'll follow these steps:
Let's work through each step:
Step 1: Identify the Common Factor
Looking at the terms , , and , the common factor among them is clearly since:
Step 2: Factor Out the Common Factor
Factoring out of each term, we rewrite the expression:
.
This simplifies to:
.
Step 3: Compare with Choices
We compare our factored expression, , to the given choices. We find that Choice 1 matches our factored form.
Therefore, the expression is equivalent to .
Which of the expressions are equal to the expression?
Let's determine the equivalence of different expressions to by factorization:
Step 1: Factor the given expression:
The expression has a common factor of .
Factor out , we obtain:
Step 2: Compare with each option:
Option 1:
This is identical to the factorized form , so it is equivalent.
Option 2:
Although it appears reversed, is equivalent to , so it's equivalent.
Option 3:
By rearranging:
It matches the original expression, thus is equivalent.
Option 4:
Expanding:
Does not match , so not equivalent.
Conclusion: The expressions equivalent to are Options 1, 2, and 3.
Therefore, the solution to the problem is .
Which of the expressions are equal to the expression?
Let's start by factoring the given expression .
First, notice that:
In the first two terms: , we can factor out , giving us .
In the last two terms: , we can factor out , resulting in .
Combining both factorizations, we can write the original expression as:
Now, we factor out the common term :
Thus, the expression simplifies to:
Now, let's verify which options match:
Option 1:
This directly matches our simplified expression, so it is a correct choice.
Option 2:
Simplifying: Factoring 3 from gives , which matches the expression . So, this is also a correct choice.
Option 3:
The factors do not align with our expression because is not factored from .
Option 4:
Rewriting: which matches. Therefore, it is correct.
Hence, options 1, 2, and 4 are equivalent to the original expression.
The correct answer to the problem is
Which of the following expressions have the same value?
\( (6b+3)(-2+a) \)
\( (2b+1)(3a-6) \)
\( (a+3)(6b-2) \)
\( 6ab+3a-12b-6 \)
Which of the expressions are equal to the expression?
\( \frac{14m^{}}{n}+21m^2 \)
\( 7m(\frac{2}{n}+3m) \)
\( 7(\frac{2}{nm}+3m^2) \)
\( \frac{m}{n}(14+3m) \)
\( 7\frac{m}{n}(2+3mn) \)
Which of the expressions are equal to the expression?
\( \frac{36t}{r}-18rt^2 \)
\( 18(\frac{2t}{r}-rt^2) \)
\( 18r(\frac{2t}{r^2}-t^2) \)
\( -18(rt+\frac{2t}{r}) \)
\( 6t(\frac{6t}{r}-3rt) \)
Which of the expressions are equal to the expression?
\( 6x^2+8xy \)
\( -2(-3x^2-4xy) \)
\( 2(3x^2+4xy) \)
\( 2x(3x+4y) \)
\( 2y(\frac{3x^2}{y}+4x) \)
Which of the following expressions have the same value?
To solve this problem, we need to systematically expand and simplify each expression given in the problem statement:
Expression 1:
Expand using the distributive property:
Reorder terms:
Expression 2:
Expand using the distributive property:
This simplifies directly to
Expression 3:
Expand using the distributive property:
This results in , clearly different from the others
Expression 4:
This is already simplified and the same as the results of expressions 1 and 2.
Upon comparing the simplified expressions, expressions 1, 2, and 4 have the same value: . Expression 3 differs with .
Thus, the expressions with the same value are 1, 2, and 4.
Therefore, the correct answer is choice 4: .
Which of the expressions are equal to the expression?
To solve this problem, we'll simplify and compare the given expressions. Let's begin by factoring the original expression:
Factor the original expression :
Notice both terms contain a factor of :
Now, let's examine each given choice:
; note this is different from the original expression since we require in the first term.
; for equivalence, recall we needed complete , not
Bifurcation gives ; multipliers yield the original expression accurately.
Thus, the answer is clearly seen that both choices 1 and 4 are equivalent to the original expression:
The correct choices are 1 and 4.
Which of the expressions are equal to the expression?
To solve this problem, let's simplify and factor the given expression:
Original expression:
Step 1: Factor out the greatest common divisor, which is 18:
This matches the structure of choice 1.
Step 2: Substitute this back into the given options and simplify.
Option 1:
This is identical to the factored form of the original.
Option 2:
Expand and simplify:
This matches the original expression.
Option 3:
Expand and simplify:
This does not match the original expression.
Option 4:
Expand and simplify:
This does not match the original expression.
Therefore, the correct options that are equivalent to the given expression are 1 and 2.
Which of the expressions are equal to the expression?
All expressions are equal