Simplify the Expression: Y² + Y⁶ - Y⁵Y Polynomial Problem

Q: Why don't I add the exponents in Y² + Y⁶?

You only add exponents when multiplying terms with the same base. When you're adding terms like $ Y^2 + Y^6 $, they stay separate unless they have identical exponents.

Q: How do I know when Y⁶ - Y⁶ equals zero?

When you have identical terms being subtracted, they always cancel out to zero. Think of it like 5 apples minus 5 apples = 0 apples!

Q: What if the exponents were different, like Y³ · Y²?

You'd still add the exponents: $ Y^3 \cdot Y^2 = Y^{3+2} = Y^5 $. The rule always works when multiplying terms with the same base.

Q: Can I simplify this expression further than Y²?

No, $ Y^2 $ is already in its simplest form. There are no like terms left to combine and no common factors to pull out.

Q: What happens if I multiply Y² · Y instead?

You'd get $ Y^2 \cdot Y^1 = Y^{2+1} = Y^3 $. Remember that $ Y = Y^1 $, so you're adding 2 + 1 = 3.

Polynomial Simplification with Exponent Rules

Solve the exercise:

$Y^2+Y^6-Y^5\cdot Y=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's simplify this expression.

00:11 Using power laws, when we multiply terms with the same base, like A,

00:16 we add the exponents. So, A to the power of N times A to the power of M becomes, A to the power of N plus M.

00:24 Let's apply this rule to our problem.

00:27 We have the same base, Y, with exponents of 5 and 1.

00:32 Since there's multiplication, we add these exponents together.

00:37 Continue solving based on the order of operations. Keep going, you're doing great!

00:47 And that's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the exercise:

$Y^2+Y^6-Y^5\cdot Y=$

Step-by-step solution

We use the power property to multiply terms with identical bases:

$a^m\cdot a^n=a^{m+n}$ We apply it in the problem:

$Y^2+Y^6-Y^5\cdot Y=Y^2+Y^6-Y^{5+1}=Y^2+Y^6-Y^6=Y^2$ When we apply the previous property to the third expression from the left in the sum, and then simplify the total expression by adding like terms.

Therefore, the correct answer is option D.

Final Answer

$Y^2$

Key Points to Remember

Essential concepts to master this topic

Exponent Rule: When multiplying same bases, add exponents: $a^m \cdot a^n = a^{m+n}$
Technique: Apply rule to $Y^5 \cdot Y = Y^{5+1} = Y^6$
Check: Combine like terms: $Y^2 + Y^6 - Y^6 = Y^2$ ✓

Common Mistakes

Avoid these frequent errors

Adding exponents in all terms instead of just multiplication
Don't add exponents when terms are just added together like Y² + Y⁶ = Y⁸! This completely changes the expression and gives wrong answers. Always add exponents only when multiplying terms with the same base.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why don't I add the exponents in Y² + Y⁶?

You only add exponents when multiplying terms with the same base. When you're adding terms like $Y^2 + Y^6$ , they stay separate unless they have identical exponents.

How do I know when Y⁶ - Y⁶ equals zero?

When you have identical terms being subtracted, they always cancel out to zero. Think of it like 5 apples minus 5 apples = 0 apples!

What if the exponents were different, like Y³ · Y²?

You'd still add the exponents: $Y^3 \cdot Y^2 = Y^{3+2} = Y^5$ . The rule always works when multiplying terms with the same base.

Can I simplify this expression further than Y²?

No, $Y^2$ is already in its simplest form. There are no like terms left to combine and no common factors to pull out.

What happens if I multiply Y² · Y instead?

You'd get $Y^2 \cdot Y^1 = Y^{2+1} = Y^3$ . Remember that $Y = Y^1$ , so you're adding 2 + 1 = 3.

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Simplify the Expression: Y² + Y⁶ - Y⁵Y Polynomial Problem

Polynomial Simplification with Exponent Rules

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why don't I add the exponents in Y² + Y⁶?

How do I know when Y⁶ - Y⁶ equals zero?

What if the exponents were different, like Y³ · Y²?

Can I simplify this expression further than Y²?

What happens if I multiply Y² · Y instead?

🌟 Unlock Your Math Potential

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