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How Can We Easily Identify and Combine Like Terms in Algebraic Expressions?

To understand how to find and combine like terms in algebra, we first need to know what "like terms" are.

What Are Like Terms?

Like terms are parts of an expression that have the same variable raised to the same power.

For example, in the expression (3x + 5x), both parts use the variable (x) to the first power. So, these two are like terms and can be combined.

Step 1: Recognizing Like Terms

The first thing to do is look for terms that have the same variable and power. Here’s a simple way to think about it:

  • Like Terms: These are terms with the same variable and the same power.
    • Example: (4y) and (2y) can be combined.
  • Not Like Terms: These are terms with different variables or powers.
    • Example: (3y) and (5x) cannot be combined.

Step 2: Grouping Like Terms

After you find like terms, the next step is to group them together to make things simpler.

Let’s look at this example:

[2a + 3b + 4a - b.]

Here, the like terms are (2a) and (4a), as well as (3b) and (-b).

So, we can group them like this:

  • For the (a) terms: (2a + 4a).
  • For the (b) terms: (3b - b).

Step 3: Combining Like Terms

Now that we've grouped the like terms, we can add them together.

  1. For the (a) terms: [2a + 4a = 6a.]

  2. For the (b) terms: [3b - b = 3b - 1b = 2b.]

Putting everything together, we simplify the whole expression: [2a + 3b + 4a - b = 6a + 2b.]

Example for Practice

Let’s look at another expression:

[5x^2 + 3x + 2x^2 - 4x + 7.]

1. Find the Like Terms:

  • For (x^2): (5x^2) and (2x^2).
  • For (x): (3x) and (-4x).
  • The number (7) is a constant (it doesn't have any like terms).

2. Group Them Together:

  • Group the (x^2) terms: (5x^2 + 2x^2).
  • Group the (x) terms: (3x - 4x).

3. Combine Them:

  • For the (x^2) terms: [5x^2 + 2x^2 = 7x^2.]

  • For the (x) terms: [3x - 4x = -1x = -x.]

So, the simplified expression is: [5x^2 + 3x + 2x^2 - 4x + 7 = 7x^2 - x + 7.]

Practice Makes Perfect

The more you practice finding and combining like terms, the easier it will get! Start with simple problems and then try harder ones. Always look for terms with the same variable raised to the same power. Soon, simplifying algebraic expressions will feel very easy!

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How Can We Easily Identify and Combine Like Terms in Algebraic Expressions?

To understand how to find and combine like terms in algebra, we first need to know what "like terms" are.

What Are Like Terms?

Like terms are parts of an expression that have the same variable raised to the same power.

For example, in the expression (3x + 5x), both parts use the variable (x) to the first power. So, these two are like terms and can be combined.

Step 1: Recognizing Like Terms

The first thing to do is look for terms that have the same variable and power. Here’s a simple way to think about it:

  • Like Terms: These are terms with the same variable and the same power.
    • Example: (4y) and (2y) can be combined.
  • Not Like Terms: These are terms with different variables or powers.
    • Example: (3y) and (5x) cannot be combined.

Step 2: Grouping Like Terms

After you find like terms, the next step is to group them together to make things simpler.

Let’s look at this example:

[2a + 3b + 4a - b.]

Here, the like terms are (2a) and (4a), as well as (3b) and (-b).

So, we can group them like this:

  • For the (a) terms: (2a + 4a).
  • For the (b) terms: (3b - b).

Step 3: Combining Like Terms

Now that we've grouped the like terms, we can add them together.

  1. For the (a) terms: [2a + 4a = 6a.]

  2. For the (b) terms: [3b - b = 3b - 1b = 2b.]

Putting everything together, we simplify the whole expression: [2a + 3b + 4a - b = 6a + 2b.]

Example for Practice

Let’s look at another expression:

[5x^2 + 3x + 2x^2 - 4x + 7.]

1. Find the Like Terms:

  • For (x^2): (5x^2) and (2x^2).
  • For (x): (3x) and (-4x).
  • The number (7) is a constant (it doesn't have any like terms).

2. Group Them Together:

  • Group the (x^2) terms: (5x^2 + 2x^2).
  • Group the (x) terms: (3x - 4x).

3. Combine Them:

  • For the (x^2) terms: [5x^2 + 2x^2 = 7x^2.]

  • For the (x) terms: [3x - 4x = -1x = -x.]

So, the simplified expression is: [5x^2 + 3x + 2x^2 - 4x + 7 = 7x^2 - x + 7.]

Practice Makes Perfect

The more you practice finding and combining like terms, the easier it will get! Start with simple problems and then try harder ones. Always look for terms with the same variable raised to the same power. Soon, simplifying algebraic expressions will feel very easy!

Related articles