Question
\( - 2 x ^ { 2 } y ^ { 3 } + 4 x ^ { 3 } y ^ { 2 } = - 2 x ^ { 2 } y ^ { 2 } ( \)
Ask by Huff Dawson. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression factors to \( -2x^2y^2(y - 2x) \).
Solution
To factor the expression
–2x²y³ + 4x³y²
follow these steps:
1. Identify the greatest common factor (GCF) of each term. Here, each term has at least:
• a factor of 2
• a factor of x²
• a factor of y²
2. We also choose the common factor to be –2x²y² so that when we factor it out, the signs inside the parentheses become simpler.
3. Factor –2x²y² from each term:
• –2x²y³ can be written as –2x²y² · y
• 4x³y² can be written as –2x²y² · (–2x)
4. Therefore, the expression factors as:
–2x²y² (y – 2x)
This is the fully factored form of the given expression.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
Did you know that the process of factoring polynomials like this one has been around since ancient civilizations? The Babylonians were already using rudimentary forms of algebra more than 4,000 years ago, and the pursuit of solving quadratic equations led to the development of algebraic notation we use today! In the real world, factoring can simplify complex problems. For instance, engineers often need to factor expressions to optimize designs, such as minimizing surface area while maximizing strength. By transforming equations into their factored forms, they can identify key variables affecting the performance of structures. Isn't math cool?
