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. $ac+4a+bc+4b$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Open brackets

00:03 Open brackets properly, multiply each factor by each factor

00:14 Calculate the multiplications, and group the factors

00:21 This is the simplification for 1, let's continue to 2

00:27 Open brackets properly, multiply each factor by each factor

00:32 Calculate the multiplications, and group the factors

00:38 This is the simplification for 2, let's continue to 3

00:42 Open brackets properly, multiply each factor by each factor

00:50 Calculate the multiplications, and group the factors

00:53 This is the simplification for 3, let's continue to 4

01:00 Open brackets properly, multiply each factor by each factor

01:03 Calculate the multiplications, and group the factors

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

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

$$ (x+y)(x-y)= $$

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.

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