Match Equivalent Expressions: (a±b)(c±4) Expansions

Q: How do I keep track of all the signs when expanding?

Use the FOIL method systematically: First × First, Outer × Outer, Inner × Inner, Last × Last. Write each step: $ (a-b)(c+4) = ac + 4a + (-b)(c) + (-b)(4) $.

Q: Why do some terms become positive and others negative?

It depends on the signs being multiplied! Remember: positive × positive = positive, negative × negative = positive, but positive × negative = negative. Track each multiplication carefully.

Q: What's the easiest way to check my expansion?

Pick simple values like a=1, b=1, c=1 and substitute into both the original expression and your expanded form. If they give the same result, you're correct!

Q: Do I always get four terms when expanding binomials?

Usually yes, but sometimes terms can combine if they're like terms. In these problems, all four terms are different so you'll always have exactly four terms in the final answer.

Q: How do I match the expressions to the right expansions?

Expand each binomial product step by step, then compare term by term with the given options. Look for the same coefficients and signs in the same positions: ac term, a term, bc term, and constant term.

Binomial Expansion with Sign Patterns

Join expressions of equal value

$(a-b)(c-4)$
$(a+b)(c+4)$
$(a-b)(c+4)$
$(a+b)(c-4)$
a. $ac-4a+bc-4b$
b. $ac+4a-bc-4b$
c. $ac-4a-bc+4b$
d. $ac+4a+bc+4b$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:30 Let's start by opening the brackets.

00:33 Carefully multiply each term by every other term.

00:44 After that, add up all the products and simplify.

00:51 Great job! That's the first part. Let's move to the next one.

00:57 Again, open the brackets and multiply every term together.

01:02 Now, sum up the products and simplify the expression.

01:08 Well done! That's the second part. Onwards to the third.

01:13 Open the brackets again and multiply each term.

01:20 Now, combine the products and simplify.

01:23 Awesome work! That's the third part. Let's finish with the last one .

01:30 Open the brackets once more and multiply each term.

01:35 Add the results together and simplify the expression.

01:40 And there you have it! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Join expressions of equal value

$(a-b)(c-4)$
$(a+b)(c+4)$
$(a-b)(c+4)$
$(a+b)(c-4)$
a. $ac-4a+bc-4b$
b. $ac+4a-bc-4b$
c. $ac-4a-bc+4b$
d. $ac+4a+bc+4b$

Step-by-step solution

We use all the exercises of the extended distributive property: $(a+b)\times(c+d)=ac+ad+bc+bd$

1. $(a-b)(c-4)=ac-4a-bc+4b$

2. $(a+b)(c+4)=ac+4a+bc+4b$

3. $(a-b)(c+4)=ac+4a-bc-4b$

4. $(a+b)(c-4)=ac-4a+bc-4b$

Final Answer

1-c, 2-d, 3-b, 4-a

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last terms multiply systematically
Sign Rules: $(a-b)(c+4) = ac + 4a - bc - 4b$ follows pattern
Verification: Check each term matches: ac term, constant multiple, cross terms ✓

Common Mistakes

Avoid these frequent errors

Incorrect sign handling in middle terms
Don't forget to apply negative signs to both terms when distributing = wrong signs throughout! Students often write (a-b)(c+4) as ac + 4a + bc + 4b, missing the negative on bc. Always carefully track each sign through every multiplication step.

Practice Quiz

Test your knowledge with interactive questions

It is possible to use the distributive property to simplify the expression below?

What is its simplified form?

$$ (ab)(c d) $$

$$

FAQ

Everything you need to know about this question

How do I keep track of all the signs when expanding?

Use the FOIL method systematically: First × First, Outer × Outer, Inner × Inner, Last × Last. Write each step: $(a-b)(c+4) = ac + 4a + (-b)(c) + (-b)(4)$ .

Why do some terms become positive and others negative?

It depends on the signs being multiplied! Remember: positive × positive = positive, negative × negative = positive, but positive × negative = negative. Track each multiplication carefully.

What's the easiest way to check my expansion?

Pick simple values like a=1, b=1, c=1 and substitute into both the original expression and your expanded form. If they give the same result, you're correct!

Do I always get four terms when expanding binomials?

Usually yes, but sometimes terms can combine if they're like terms. In these problems, all four terms are different so you'll always have exactly four terms in the final answer.

How do I match the expressions to the right expansions?

Expand each binomial product step by step, then compare term by term with the given options. Look for the same coefficients and signs in the same positions: ac term, a term, bc term, and constant term.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Technique questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime