(2x+5y)(3x-2y)(5x+y)

2 min read Jun 16, 2024
(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.

Related Post


Featured Posts