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(x+y)(2x+y)+(x+2y)(x-y) Solve

2 min read Jun 17, 2024
(x+y)(2x+y)+(x+2y)(x-y) Solve

Simplifying the Expression: (x+y)(2x+y)+(x+2y)(x-y)

This problem involves expanding and simplifying an algebraic expression. Let's break it down step by step:

Step 1: Expanding the Expressions

We can expand the expressions using the FOIL method (First, Outer, Inner, Last).

  • (x+y)(2x+y):

    • First: x * 2x = 2x²
    • Outer: x * y = xy
    • Inner: y * 2x = 2xy
    • Last: y * y = y²
    • Combined: 2x² + xy + 2xy + y² = 2x² + 3xy + y²

  • (x+2y)(x-y):

    • First: x * x = x²
    • Outer: x * -y = -xy
    • Inner: 2y * x = 2xy
    • Last: 2y * -y = -2y²
    • Combined: x² - xy + 2xy - 2y² = x² + xy - 2y²

Step 2: Combining Like Terms

Now, we have: (2x² + 3xy + y²) + (x² + xy - 2y²)

Combining the terms with the same variables and exponents:

  • x² terms: 2x² + x² = 3x²
  • xy terms: 3xy + xy = 4xy
  • y² terms: y² - 2y² = -y²

Step 3: The Final Solution

Putting it all together, the simplified expression is:

(x+y)(2x+y)+(x+2y)(x-y) = 3x² + 4xy - y²

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