Simplify the Expression: Y² + Y⁶ - Y⁵Y Polynomial Problem

Question

Solve the exercise:

Y2+Y6−Y5⋅Y= Y^2+Y^6-Y^5\cdot Y=

Video Solution

Solution Steps

00:00 Simplify the expression
00:03 According to 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 to the question
00:13 The same base(Y) with exponents(5,1)
00:17 Because there's multiplication between them, we'll add the exponents
00:24 We'll continue solving according to proper order of operations
00:39 And this is the solution to the question

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.

Answer

Y2 Y^2

More Questions

Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Multiplying Exponents with the Same Base

Question Types

Multiplication of Powers: Solving the problem Multiplication of Powers: Variable in the base of the power Multiplication of Powers: Applying the formula Applying Combined Exponents Rules: Multiplying Exponents with the same base Applying Combined Exponents Rules: Single Variable Applying Combined Exponents Rules: Using the laws of exponents Applying Combined Exponents Rules: Variable in the base of the power Applying Combined Exponents Rules: Applying the formula Applying Combined Exponents Rules: A power law