Algebraic Identities Math Example 1

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

Example 1

easy
Expand (x+3)2(x + 3)^2 using the identity (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2.

Solution

  1. 1
    Step 1: a=xa = x, b=3b = 3.
  2. 2
    Step 2: (x+3)2=x2+2(x)(3)+32=x2+6x+9(x+3)^2 = x^2 + 2(x)(3) + 3^2 = x^2 + 6x + 9.
  3. 3
    Check: (x+3)(x+3)=x2+3x+3x+9=x2+6x+9(x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9 ✓

Answer

x2+6x+9x^2 + 6x + 9
Algebraic identities are equations that hold for all values of the variables. The perfect square identity (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2 is faster than FOIL for squaring binomials.

About Algebraic Identities

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

Learn more about Algebraic Identities →

More Algebraic Identities Examples

Example 2 medium

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

Example 3 easy

Expand [formula].

Example 4 hard

Factor [formula] using the sum of cubes identity.

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