Simplify the Polynomial Expression: 7y² - 3y + 4

Polynomial Simplification with Unlike Terms

Simplify the expression:

7y23y+4 7y^2 - 3y + 4

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Simplify the expression:

7y23y+4 7y^2 - 3y + 4

2

Step-by-step solution

The expression is already in its simplest form as it consists of terms where none can be combined due to differing degrees of the variable y y . Thus, the simplified expression is: 7y23y+4 7y^2 - 3y + 4 .

3

Final Answer

7y23y+4 7y^2 - 3y + 4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Only combine terms with identical variable powers and coefficients
  • Technique: Check each term: 7y², -3y, and 4 have different degrees
  • Check: Count terms before and after: 3 terms remain = already simplified ✓

Common Mistakes

Avoid these frequent errors
  • Trying to combine terms with different variable powers
    Don't add 7y² + (-3y) = 4y² because they have different exponents! This creates an incorrect expression that changes the polynomial's value. Always only combine like terms with identical variable parts and powers.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

\( 4x^2 + 6x \)

FAQ

Everything you need to know about this question

Why can't I combine 7y² and -3y together?

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You can only combine like terms - terms with exactly the same variable and exponent. Since 7y2 7y^2 has y² and 3y -3y has y¹, they're different types of terms!

What makes terms 'like terms' that can be combined?

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Like terms must have:

  • The same variable (like y)
  • The same exponent (like y² with y² or y with y)
  • Only the coefficients can be different

Is 7y² - 3y + 4 really the final answer?

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Yes! When no terms can be combined, the expression is already simplified. Think of it like organizing different objects - you can't combine apples, oranges, and bananas into one item.

How do I know when a polynomial is fully simplified?

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A polynomial is simplified when:

  • No two terms have the same variable part
  • Terms are arranged in descending order by degree
  • All coefficients are in simplest form

What if I had 7y² + 2y² - 3y + 4 instead?

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Then you could combine the like terms! 7y2+2y2=9y2 7y^2 + 2y^2 = 9y^2 , giving you 9y23y+4 9y^2 - 3y + 4 as the simplified form.

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