Solve: (-4-y)(-2x-?) = 8x-16-4y+2xy - Finding the Missing Term

Q: How do I know which terms to multiply together?

Use the FOIL method for binomials: multiply First terms, then Outer terms, then Inner terms, then Last terms. Each term in the first parentheses multiplies each term in the second.

Q: What if I get confused with the negative signs?

Take it step by step! Remember that negative × negative = positive and negative × positive = negative. Write out each multiplication separately: $ (-4) \times (-2x) = +8x $.

Q: Why does the order of terms matter when comparing?

The order doesn't matter mathematically! $ 8x - 16 - 4y + 2xy $ equals $ 8x + 2xy - 4y - 16 $. Focus on making sure all terms match, regardless of their position.

Q: What if I can't figure out the missing term?

Set up equations by comparing coefficients! If you need $ -4? = -16 $, then $ ? = \frac{-16}{-4} = 4 $. Work backwards from what you want to achieve.

Polynomial Expansion with Missing Terms

Complete the missing element

$(-4-y)(-2x-?)=8x-16-4y+2xy$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing term

00:04 Substitute A as unknown

00:09 Open parentheses properly, multiply each factor by each factor

00:28 Calculate the products

00:46 Compare the corresponding terms

00:53 Isolate the unknown A

00:59 This is the value of A, now let's check if it fits

01:05 Compare the corresponding terms, find the value of A we found

01:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the missing element

$(-4-y)(-2x-?)=8x-16-4y+2xy$

Step-by-step solution

To solve for the missing element, we'll employ the distributive property as follows:

1. Let's expand $(-4-y)(-2x-?)$ :

Multiply $-4$ by $-2x$ : $-4 \times -2x = 8x$ .
Multiply $-4$ by the unknown: $-4 \times ? = -4?$ .
Multiply $-y$ by $-2x$ : $-y \times -2x = 2xy$ .
Multiply $-y$ by the unknown: $-y \times ? = -y?$ .

2. Combine these results to form the expression:

8x - 4? + 2xy - y?

3. Compare this expression with the target expression $8x - 16 - 4y + 2xy$ :

We already have $8x$ and $2xy$ matching, so we're left to make the terms $-4?$ and $-y?$ match $-16$ and $-4y$ respectively.

4. From $-4? = -16$ , we solve for $?$ :

-4? = -16 \rightarrow ? = \frac{-16}{-4} = 4

Thus, the missing number $-4$ is needed to get the resulting expression to match.

Therefore, the missing element is $\boxed{-4}$ .

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Each term in first parentheses multiplies each term in second
Expansion Method: (-4)(-2x) = 8x and (-4)(?) = -4? for unknown
Verification: Check by comparing expanded form 8x - 4? + 2xy - y? with target ✓

Common Mistakes

Avoid these frequent errors

Not distributing all terms systematically
Don't randomly multiply terms or skip the distributive steps = missing or incorrect terms! This leads to equations that don't balance properly. Always multiply each term in the first parentheses by every term in the second parentheses systematically.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

How do I know which terms to multiply together?

Use the FOIL method for binomials: multiply First terms, then Outer terms, then Inner terms, then Last terms. Each term in the first parentheses multiplies each term in the second.

What if I get confused with the negative signs?

Take it step by step! Remember that negative × negative = positive and negative × positive = negative. Write out each multiplication separately: $(-4) \times (-2x) = +8x$ .

How do I check if my missing term is correct?

Substitute your answer back into the original expression and expand completely. If your expanded form matches $8x - 16 - 4y + 2xy$ exactly, you found the right missing term!

Why does the order of terms matter when comparing?

The order doesn't matter mathematically! $8x - 16 - 4y + 2xy$ equals $8x + 2xy - 4y - 16$ . Focus on making sure all terms match, regardless of their position.

What if I can't figure out the missing term?

Set up equations by comparing coefficients! If you need $-4? = -16$ , then $? = \frac{-16}{-4} = 4$ . Work backwards from what you want to achieve.

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