Find Equivalent Expressions for 16-4c: Algebraic Comparison

Q: How do I find the greatest common factor of 16 and 4c?

Look at the numerical coefficients only: 16 and 4. The GCF is the largest number that divides both evenly. Since 4 goes into both 16 and 4, the GCF is 4.

Q: Why can't I factor out 8 or 2 instead?

You could factor out 2: $ 2(8-2c) $, but this isn't fully factored. The greatest common factor gives you the simplest form, which is what most problems ask for.

Q: What if the variable term was positive, like 16+4c?

The process is the same! Factor out 4: $ 16+4c = 4(4+c) $. The sign stays positive inside the parentheses.

Q: How can I check if my factored form is correct?

Use the distributive property in reverse! Multiply 4 by each term inside: $ 4(4-c) = 4 \times 4 - 4 \times c = 16-4c $. If you get the original expression, you're right!

Q: What if there's no common factor between terms?

If the GCF is 1 (like in $ 5x + 7 $), then the expression is already in simplest form and cannot be factored further using this method.

Factoring with Greatest Common Factor

Which of the expressions is equivalent to the expression?

$16-4c$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find a common factor. Ready?

00:11 Break down 16 into 4 times 4.

00:16 Now, identify the common factors. Great job!

00:24 Take these common factors outside the parentheses.

00:29 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the expressions is equivalent to the expression?

$16-4c$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the greatest common factor (GCF) of the terms in the expression $16 - 4c$ .
Step 2: Factor out the GCF from both terms.
Step 3: Compare the factored expression with the provided choices to find the equivalent expression.

Let's work through each step:

Step 1: Identify the GCF.
The terms in the expression are $16$ and $-4c$ . The greatest common factor of $16$ and $4$ (coefficient of $c$ ) is $4$ .

Step 2: Factor out the GCF.
Factor $4$ out from each term in the expression:
$16 - 4c = 4 \times 4 - 4 \times c = 4(4 - c)$ .

Step 3: Compare with the choices.
We factorized $16 - 4c$ to get $4(4 - c)$ . Now we compare it with the provided choices:

Choice 1: $4(12 - c)$ does not match our expression.
Choice 2: $4(4 - 4c)$ is also not equivalent.
Choice 3: $4(2 - c)$ is not equivalent.
Choice 4: $4(4 - c)$ matches our expression precisely.

Therefore, the expression equivalent to $16 - 4c$ is $\boxed{4(4 - c)}$ .

Final Answer

$4(4-c)$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the GCF of all terms first
Technique: Factor out 4 from both terms: $16 = 4 \times 4$ and $4c = 4 \times c$
Check: Distribute to verify: $4(4-c) = 16-4c$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to factor out the negative sign properly
Don't write 4(4+c) when factoring 16-4c = wrong sign on c term! The negative must stay with the c term inside the parentheses. Always keep the original signs when factoring out the GCF.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 4x^2 + 6x $$

FAQ

Everything you need to know about this question

How do I find the greatest common factor of 16 and 4c?

Look at the numerical coefficients only: 16 and 4. The GCF is the largest number that divides both evenly. Since 4 goes into both 16 and 4, the GCF is 4.

Why can't I factor out 8 or 2 instead?

You could factor out 2: $2(8-2c)$ , but this isn't fully factored. The greatest common factor gives you the simplest form, which is what most problems ask for.

What if the variable term was positive, like 16+4c?

The process is the same! Factor out 4: $16+4c = 4(4+c)$ . The sign stays positive inside the parentheses.

How can I check if my factored form is correct?

Use the distributive property in reverse! Multiply 4 by each term inside: $4(4-c) = 4 \times 4 - 4 \times c = 16-4c$ . If you get the original expression, you're right!

What if there's no common factor between terms?

If the GCF is 1 (like in $5x + 7$ ), then the expression is already in simplest form and cannot be factored further using this method.

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