(3x-2y)(5x%2By).jpeg "(2x+5y)(3x-2y)(5x+y)")
Expanding the Expression: (2x+5y)(3x-2y)(5x+y)
This article explores how to expand the given expression: (2x+5y)(3x-2y)(5x+y). We'll use the distributive property and simplify the result.
Step 1: Expand the first two factors
First, we expand the first two factors using the distributive property (FOIL method).
- First: 2x * 3x = 6x²
- Outer: 2x * -2y = -4xy
- Inner: 5y * 3x = 15xy
- Last: 5y * -2y = -10y²
Combining these terms, we get: (2x+5y)(3x-2y) = 6x² + 11xy - 10y²
Step 2: Expand the result with the third factor
Now we have: (6x² + 11xy - 10y²)(5x+y)
Again, we use the distributive property:
- 6x² * 5x = 30x³
- 6x² * y = 6x²y
- 11xy * 5x = 55x²y
- 11xy * y = 11xy²
- -10y² * 5x = -50xy²
- -10y² * y = -10y³
Step 3: Simplify the result
Finally, we combine like terms to get the fully expanded expression:
(2x+5y)(3x-2y)(5x+y) = 30x³ + 61x²y + xy² - 10y³
Therefore, the expanded form of the given expression is 30x³ + 61x²y + xy² - 10y³.