Expansion Intuition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Expand (x−2)(x+7)(x - 2)(x + 7).

Solution

  1. 1
    FOIL: x2+7x−2x−14=x2+5x−14x^2 + 7x - 2x - 14 = x^2 + 5x - 14.
  2. 2
    Check: −2+7=5-2 + 7 = 5 and (−2)(7)=−14(-2)(7) = -14 ✓

Answer

x2+5x−14x^2 + 5x - 14
Multiply each term in the first binomial by each term in the second, then combine like terms.

About Expansion Intuition

Understanding algebraic expansion as the process of applying the distributive property to multiply out factors and remove parentheses.

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More Expansion Intuition Examples

Example 1 easy

Expand [formula].

Example 2 medium

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Example 4 medium

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