Practice Algebraic Identities in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Algebraic identities are equalities true for all permitted values of their variables.
Identities are always-true shortcuts — no matter what values you substitute, both sides will always be equal.
Example 1
easyExpand (x + 3)^2 using the identity (a+b)^2 = a^2 + 2ab + b^2.
Example 2
mediumCompute 47^2 mentally using (a - b)^2 = a^2 - 2ab + b^2 with a = 50, b = 3.
Example 3
easyExpand (2x - 5)^2.
Example 4
hardFactor x^3 + 8 using the sum of cubes identity.