Expand the Expression: Step-by-Step Solution for (a+4)(c+3)

Binomial Multiplication with Distribution Property

(a+4)(c+3)= (a+4)(c+3)=

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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 Calculate the multiplications
00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(a+4)(c+3)= (a+4)(c+3)=

2

Step-by-step solution

When we encounter a multiplication exercise of this type, we know that we must use the distributive property.

Step 1: Multiply the first factor of the first parentheses by each of the factors of the second parentheses.

Step 2: Multiply the second factor of the first parentheses by each of the factors of the second parentheses.

Step 3: Group like terms.

a * (c+3) =

a*c + a*3

4 * (c+3) =

4*c + 4*3

ac+3a+4c+12

There are no like terms to simplify here, so this is the solution!

3

Final Answer

ac+3a+4c+12 ac+3a+4c+12

Key Points to Remember

Essential concepts to master this topic
  • Distribution Rule: Each term in first binomial multiplies each term in second
  • FOIL Method: First (ac), Outer (3a), Inner (4c), Last (12) terms
  • Check: Count 4 terms total: ac + 3a + 4c + 12 ✓

Common Mistakes

Avoid these frequent errors
  • Only multiplying first terms or forgetting middle terms
    Don't just multiply a×c = ac and 4×3 = 12! This misses the crucial middle terms 3a and 4c, giving you ac + 12 instead of the complete answer. Always distribute each term from the first parentheses to every term in the second parentheses.

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 4 terms when multiplying two binomials?

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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 multiplication operations, giving you 4 terms total!

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

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FOIL is just a memory trick for the distributive property! It helps you remember: First, Outer, Inner, Last terms. Both methods give the same answer.

Do I always need to arrange the terms in a specific order?

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No! ac+3a+4c+12 ac + 3a + 4c + 12 is the same as 3a+ac+12+4c 3a + ac + 12 + 4c . The order doesn't matter as long as you have all 4 terms.

How can I check if I distributed correctly?

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Count your terms! You should have exactly 4 terms when multiplying two binomials. Also, substitute simple numbers like a=1, c=1 to verify: (1+4)(1+3) = 5×4 = 20, and 1+3+4+12 = 20 ✓

What if some terms can be combined?

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In this problem, no terms can be combined because ac, 3a, 4c, and 12 are all different types. Only combine terms with exactly the same variables and exponents!

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