One of the fundamental polynomial identities in basic algebra is the square of a trinomial, which is mathematically represented as $(a + b + c)^2$. Knowing how to expand this helps in geometry, quadratic equations, and calculus.
It is known as the Square of a Trinomial.
The formula applies to real numbers, complex numbers, and matrices (if commutative).
If any variable is negative (like $a - b + c$), the sign of the product terms ($2ab$, $2bc$, etc.) changes accordingly.
The standard algebraic formula is:
This can also be written by factoring out the 2:
You can derive this formula by multiplying the trinomial by itself:
Following the same pattern but substituting negative signs: (a - b - c)^2 = a^2 + b^2 + c^2 - 2ab + 2bc - 2ca.
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