Math Problem Statement
-2(-x)^5(6x-9)^4((-x)^2+1))^2
Solution
Let's break down and simplify the expression you provided step by step:
Step 1: Simplify each component
Since the exponent is odd, this expression simplifies as follows:
We have already expanded in the previous step. The result was:
Here, simplifies to , so:
Now, squaring this expression gives:
Step 2: Combine the components
Now that we've simplified the individual components, we can substitute them back into the original expression:
Substituting the simplifications:
Step 3: Simplify the negative terms
We already have inside the expression. Multiplying by the negative 2 will simplify as:
So the expression becomes:
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Expansion
Exponent Rules
Quadratic Functions
Formulas
(-x)^n = (-1)^n * x^n for odd and even powers
(a-b)^n formula for binomial expansion
(a+b)^2 = a^2 + 2ab + b^2
Theorems
Exponent Laws
Polynomial Expansion Theorem
Suitable Grade Level
Grades 10-12