Expand (a+b)(c+d): Step-by-Step Binomial Multiplication

Q: Why do I get four terms when multiplying two binomials?

Because each of the 2 terms in the first binomial must multiply each of the 2 terms in the second binomial. That's 2 × 2 = 4 multiplications, giving you 4 terms!

Q: Do I need to put the terms in any special order?

No special order is required! $ ac + ad + bc + bd $ is the same as $ ad + bc + ac + bd $. The important thing is having all four terms.

Q: Is there a pattern I can memorize?

Yes! Remember FOIL for binomials: First terms, Outer terms, Inner terms, Last terms. For $ (a+b)(c+d) $: ac (First) + ad (Outer) + bc (Inner) + bd (Last).

Q: What if I forget to multiply one of the terms?

Double-check by counting! You should always get exactly 4 terms when multiplying two binomials. If you have fewer, you missed a multiplication step.

Binomial Multiplication with Distributive Property

$(a+b)(c+d)=$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

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

00:20 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

$(a+b)(c+d)=$ ?

Step-by-step solution

Let's simplify the expression by opening the parentheses using the distributive property:

$(\textcolor{red}{a}+\textcolor{blue}{b})(c+d)=\textcolor{red}{a}c+\textcolor{red}{a}d+\textcolor{blue}{b}c+\textcolor{blue}{b}d$

Therefore, the correct answer is (a).

Final Answer

$\text{ac + ad}+bc+bd$

Key Points to Remember

Essential concepts to master this topic

Distributive Rule: Each term in first binomial multiplies each term in second
Technique: Multiply systematically: a×c, a×d, b×c, b×d
Check: Count four terms in final answer: ac + ad + bc + bd ✓

Common Mistakes

Avoid these frequent errors

Only multiplying first terms and last terms
Don't just multiply a×c and b×d to get ac+bd! This skips the middle terms (cross products) and gives an incomplete answer. Always multiply each term in the first binomial by every term in the second binomial.

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 four terms when multiplying two binomials?

Because each of the 2 terms in the first binomial must multiply each of the 2 terms in the second binomial. That's 2 × 2 = 4 multiplications, giving you 4 terms!

Do I need to put the terms in any special order?

No special order is required! $ac + ad + bc + bd$ is the same as $ad + bc + ac + bd$ . The important thing is having all four terms.

What if some terms can be combined?

Great observation! If you have like terms (same variables), combine them. For example, if you get $2x + 3x$ , simplify to $5x$ .

Is there a pattern I can memorize?

Yes! Remember FOIL for binomials: First terms, Outer terms, Inner terms, Last terms. For $(a+b)(c+d)$ : ac (First) + ad (Outer) + bc (Inner) + bd (Last).

What if I forget to multiply one of the terms?

Double-check by counting! You should always get exactly 4 terms when multiplying two binomials. If you have fewer, you missed a multiplication step.

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