How to Expand Square of a Trinomial?
Expanding the square of a trinomial involves multiplying the trinomial by itself and simplifying the resulting expression. Let’s use a general trinomial (ax2 + bx + c) as an example and go through the steps to expand its square (ax2 + bx + c)2
Step 1: Apply Distributive Property
(ax2 + bx + c)2
= (ax2 + bx + c)(ax2 + bx + c)
Distribute each term in the first trinomial to every term in the second trinomial:
= a(ax2) + a(bx) + ac + b(ax2) + b(bx) + bc + c(ax2) + c(bx) + c2
Step 2: Simplify and Combine Like Terms
= a2x4 + 2abx3 + (2ac + b2)x2 + 2bcx + c2
Combine like terms to simplify the expression.
So, expanded form of (ax2 + bx + c)2 is [a2x4 + 2abx3 + (2ac + b2)x2 + 2bcx + c2]
Also Read
Squaring a Trinomial
Squaring a trinomial involves multiplying a trinomial by itself. A trinomial is an algebraic expression with three terms, typically of the form a+b+c where a, b, and c represent constants or variables.
It requires multiplying the trinomial by itself using the distributive property and then simplifying the expression by combining like terms. This process is fundamental in algebra and provides an expanded form of the trinomial.
Let’s know more Trinomial Definition, How to Square Trinomial, and Different Methods of Squaring a Trinomial with some solved examples to understand better.