Solve the Binomial Product: (-7-4y)(5x+6) Expansion Problem

Q: Why do I get so many terms when multiplying binomials?

When multiplying two binomials, each term from the first must multiply each term from the second. That's 2 × 2 = 4 terms total! Use FOIL (First, Outer, Inner, Last) to make sure you don't miss any.

Q: How do I handle the negative signs correctly?

Remember: negative × positive = negative and negative × negative = positive. In $ (-7-4y)(5x+6) $, both -7 and -4y are negative, so they make negative products with the positive terms.

Q: Can I combine any of the terms in my final answer?

Look for like terms - terms with the same variables and exponents. In $ -35x-42-20xy-24y $, all terms are different (x, constant, xy, y), so no combining is possible.

Q: What's the difference between FOIL and the distributive property?

FOIL is just a memory trick for the distributive property with binomials! It helps you remember to multiply: First terms, Outer terms, Inner terms, Last terms.

Q: Why is my answer different from the given options?

Check your sign work carefully! The most common error is getting positive terms instead of negative ones. Also verify you didn't miss any multiplication steps using FOIL.

Binomial Expansion with Negative Terms

Solve the following equation:

$(-7-4y)(5x+6)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 Let's open the parentheses properly, multiply each factor by each factor

00:41 Let's calculate the multiplications

01:16 Positive times negative always equals negative

01:27 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

Solve the following equation:

$(-7-4y)(5x+6)=$

Step-by-step solution

In order to simplify the given expression we must use the expanded distributive law as seen below:

$(a+b)(c+d)=ac+ad+bc+bd$

First, we'll perform the multiplication between the pairs of parentheses, using the mentioned distributive law, and then we'll combine like terms if possible. We'll do this whilst taking into account the correct multiplication of signs:

$(-7-4y)(5x+6)=\\ -35x-42-20xy-24y$ Therefore, the correct answer is answer A.

Final Answer

_{^{$-35x-42-20xy-24y$}}

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply each term in first binomial by each term in second binomial
FOIL Method: First (-7)(5x) = -35x, Outer (-7)(6) = -42, Inner (-4y)(5x) = -20xy, Last (-4y)(6) = -24y
Check Signs: Verify negative times positive equals negative: (-7)(5x) = -35x ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign
Don't just multiply (-7)(5x) and forget about (-7)(6) = positive 42! This ignores the negative sign and gives +42 instead of -42. Always multiply each term in the first binomial by each term in the second binomial, keeping track of signs.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I get so many terms when multiplying binomials?

When multiplying two binomials, each term from the first must multiply each term from the second. That's 2 × 2 = 4 terms total! Use FOIL (First, Outer, Inner, Last) to make sure you don't miss any.

How do I handle the negative signs correctly?

Remember: negative × positive = negative and negative × negative = positive. In $(-7-4y)(5x+6)$ , both -7 and -4y are negative, so they make negative products with the positive terms.

Can I combine any of the terms in my final answer?

Look for like terms - terms with the same variables and exponents. In $-35x-42-20xy-24y$ , all terms are different (x, constant, xy, y), so no combining is possible.

What's the difference between FOIL and the distributive property?

FOIL is just a memory trick for the distributive property with binomials! It helps you remember to multiply: First terms, Outer terms, Inner terms, Last terms.

Why is my answer different from the given options?

Check your sign work carefully! The most common error is getting positive terms instead of negative ones. Also verify you didn't miss any multiplication steps using FOIL.

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