Algebraic Identities Math Example 2

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

Example 2

medium
Compute 47247^2 mentally using (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 with a=50,b=3a = 50, b = 3.

Solution

  1. 1
    Step 1: 47=50−347 = 50 - 3.
  2. 2
    Step 2: 472=502−2(50)(3)+32=2500−300+947^2 = 50^2 - 2(50)(3) + 3^2 = 2500 - 300 + 9.
  3. 3
    Step 3: =2209= 2209.
  4. 4
    Check: 47×47=220947 \times 47 = 2209 ✓

Answer

22092209
Algebraic identities aren't just abstract — they enable mental math. By rewriting 47 as 50−350 - 3, the computation uses only simple multiplications and additions.

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 1 easy

Expand [formula] using the identity [formula].

Example 3 easy

Expand [formula].

Example 4 hard

Factor [formula] using the sum of cubes identity.

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