Answer:
To simplify the expression (1. 5p²*y + py)(1. 5p²y + p²y²) using the identity (x+a)(x+b) = x² + (a+b)x + ab, we can follow these steps:
Step 1: Identify the terms
Let's identify the terms in the given expression:
Term 1: 5p²*y
Term 2: py
Term 3: 5p²y
Term 4: p²y²
Step 2: Apply the identity
Using the identity (x+a)(x+b) = x² + (a+b)x + ab, we can rewrite the expression as follows:
Term 1 * Term 3:
(5p²*y)(5p²y) = (5p²*y)² = 25p^4y²
Term 1 * Term 4:
(5p²*y)(p²y²) = 5p²y * p²y² = 5p^4y³
Term 2 * Term 3:
(py)(5p²y) = 5p³y²
Term 2 * Term 4:
(py)(p²y²) = p³y³
Step 3: Combine like terms
Now, let's combine the like terms obtained in Step 2:
25p^4y² + 5p^4y³ + 5p³y² + p³y³
This is the simplified form of the expression (1. 5p²*y + py)(1. 5p²y + p²y²) using the identity (x+a)(x+b) = x² + (a+b)x + ab.
Please note that I noticed a typo in the original expression. The numbers "1." before each term are unnecessary and can be removed.
Explanation: