In Mathematics, an Identity is an equation that is always true, no matter what values you plug into the variables. Memorizing standard algebraic identities is crucial for solving polynomial problems quickly.
Identity: An equation that holds true for ALL values of its variables.
Most used: (a+b)(a-b) = a² - b².
Difference from Equation: An equation like 2x = 4 is only true for x=2. But (x+1)² = x²+2x+1 is an identity because it is true for any number.
These are the foundational identities that you will use throughout your math education:
As you progress, you must learn the identities involving three variables and cubes: 5. Square of a trinomial: $(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca$ 6. Cube of a sum: $(a + b)³ = a³ + b³ + 3ab(a + b)$ 7. Cube of a difference: $(a - b)³ = a³ - b³ - 3ab(a - b)$ 8. Sum/Difference of cubes:
A mathematical identity is an algebraic equation that remains true regardless of the values substituted for its variables.
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