Match Equivalent Expressions: (a+g)x+3 and Its Related Forms

Algebraic Expansion with Expression Matching

Join expressions of equal value

  1. (a+g)x+3 (a+g)x+3

  2. (x+3)(a+g) (x+3)(a+g)

  3. (ag)x3 (a-g)x-3

    a.xa+xg+3a+3g xa+xg+3a+3g

    b.ax+gx+3 ax+gx+3

    c.axgx3 ax-gx-3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Open parentheses
00:03 Open parentheses properly, multiply each factor by each factor
00:12 Calculate the products
00:16 This is the simplification for 1, let's continue to 2
00:21 This is the simplification for 1, let's continue to 2
00:26 Calculate the products
00:30 This is the simplification for 2, let's continue to 3
00:39 Open parentheses properly, multiply by each factor
00:43 Calculate the products
00:47 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

Join expressions of equal value

  1. (a+g)x+3 (a+g)x+3

  2. (x+3)(a+g) (x+3)(a+g)

  3. (ag)x3 (a-g)x-3

    a.xa+xg+3a+3g xa+xg+3a+3g

    b.ax+gx+3 ax+gx+3

    c.axgx3 ax-gx-3

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Expand each original expression using the distributive property.
  • Step 2: Compare each expansion with the given rearranged expressions to find the correct match.

Step 1: Expand each original expression.
- For Expression 1: (a+g)x+3 (a+g)x+3 expands to ax+gx+3 ax + gx + 3 .
- For Expression 2: (x+3)(a+g) (x+3)(a+g) expands to xa+xg+3a+3g xa + xg + 3a + 3g .
- For Expression 3: (ag)x3 (a-g)x-3 expands to axgx3 ax - gx - 3 .

Step 2: Match each expanded expression to the provided options:
- Expression 1: ax+gx+3 ax + gx + 3 matches with option b.
- Expression 2: xa+xg+3a+3g xa + xg + 3a + 3g matches with option a.
- Expression 3: axgx3 ax - gx - 3 matches with option c.

Therefore, the correct mapping of expressions is:
1-b, 2-a, 3-c.

3

Final Answer

1-b, 2-a, 3-c

Key Points to Remember

Essential concepts to master this topic
  • Distribution: Apply distributive property to multiply terms systematically
  • Technique: (a+g)x+3 (a+g)x+3 becomes ax+gx+3 ax+gx+3 by distributing x
  • Check: Match expanded forms with given options by comparing every term ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to distribute to all terms
    Don't distribute only to the first term in expressions like (x+3)(a+g) (x+3)(a+g) = xa+xg xa+xg only! This misses half the terms and gives incomplete expansions. Always distribute each term in the first factor to every term in the second factor.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why does (x+3)(a+g) (x+3)(a+g) expand to four terms?

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When you multiply two binomials, each term in the first binomial multiplies with each term in the second binomial. So x multiplies with both a and g, then 3 multiplies with both a and g, giving you four terms total.

How do I know if two expressions are equivalent?

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Two expressions are equivalent if they have the same terms with the same coefficients. Expand both expressions completely and check that every term matches, even if they're written in different orders.

What's the difference between xa xa and ax ax ?

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There's no difference! Multiplication is commutative, so xa=ax xa = ax . Both expressions represent the same value and can be used interchangeably.

Why do some expressions have + while others have -?

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The signs come from the original expression! When you see (ag)x (a-g)x , the minus sign distributes: a times x gives +ax +ax , but -g times x gives gx -gx .

Can I rearrange terms after expanding?

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Yes! Addition and subtraction are commutative, so you can write terms in any order. ax+gx+3 ax + gx + 3 is the same as gx+ax+3 gx + ax + 3 or 3+ax+gx 3 + ax + gx .

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