Simplify the Expression: Y² + Y⁶ - Y⁵Y Polynomial Problem

Solve the exercise:

Y2+Y6−Y5⋅Y= 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
00:00 Simplify the following expression
00:03 According to the power laws, multiplication with the same base(A) with exponents N,M
00:06 Will equal the same base(A) with exponent (N+M)
00:10 Let's apply this to the problem
00:13 The same base(Y) with exponents(5,1)
00:17 Given that there's multiplication between them, we must add the exponents
00:24 Continue to solve according to the order of operations
00:39 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the exercise:

Y2+Y6−Y5⋅Y= Y^2+Y^6-Y^5\cdot Y=

2

Step-by-step solution

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

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

Y2+Y6−Y5⋅Y=Y2+Y6−Y5+1=Y2+Y6−Y6=Y2 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.

3

Final Answer

Y2 Y^2

Practice Quiz

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\( 112^0=\text{?} \)

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