$$ - 2 x ^ { 2 } y ^ { 3 } + 4 x ^ { 3 } y ^ { 2 } = - 2 x ^ { 2 } y ^ { 2 } ( $$

Question

UpStudy AI · Accepted Answer

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.
The expression factors to $$ -2x^2y^2(y - 2x) $$.

\( - 2 x ^ { 2 } y ^ { 3 } + 4 x ^ { 3 } y ^ { 2 } = - 2 x ^ { 2 } y ^ { 2 } ( \)