Algebraic Identities Math Example 3

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

Example 3

easy
Expand (2x−5)2(2x - 5)^2.

Solution

  1. 1
    (2x)2−2(2x)(5)+52=4x2−20x+25(2x)^2 - 2(2x)(5) + 5^2 = 4x^2 - 20x + 25.
  2. 2
    Check at x=1x = 1: (2−5)2=9(2-5)^2 = 9 and 4−20+25=94 - 20 + 25 = 9 ✓

Answer

4x2−20x+254x^2 - 20x + 25
The (a−b)2(a-b)^2 identity produces a positive middle term's negative and a positive last term. Common mistake: writing −25-25 instead of +25+25.

About Algebraic Identities

Algebraic identities are equalities true for all permitted values of their variables.

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More Algebraic Identities Examples

Example 1 easy

Expand [formula] using the identity [formula].

Example 2 medium

Compute [formula] mentally using [formula] with [formula].

Example 4 hard

Factor [formula] using the sum of cubes identity.

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