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(x+y-7)2

2 min read Jun 17, 2024
(x+y-7)2

Expanding (x + y - 7)²

The expression (x + y - 7)² represents the square of a trinomial. To expand this, we can use the FOIL method (First, Outer, Inner, Last) and the distributive property.

Step 1: Rewrite the expression

(x + y - 7)² = (x + y - 7)(x + y - 7)

Step 2: Apply the FOIL method

  • First: x * x = x²
  • Outer: x * y = xy
  • Inner: x * -7 = -7x
  • Last: y * y = y²
  • Outer: y * -7 = -7y
  • Inner: -7 * x = -7x
  • Last: -7 * -7 = 49

Step 3: Combine like terms

x² + xy - 7x + y² - 7y - 7x + 49

Step 4: Simplify

x² + y² + 2xy - 14x - 14y + 49

Therefore, the expanded form of (x + y - 7)² is x² + y² + 2xy - 14x - 14y + 49.

Key Points:

  • The FOIL method is a helpful tool for expanding products of binomials.
  • Be careful when combining like terms, especially when dealing with multiple variables.
  • Remember that squaring a trinomial involves multiplying it by itself.

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