Multiplying a Binomial and a Trinomial
Multiplying a Binomial and a Trinomial
A trinomial is an expression with three terms, for example, \(a{x}^{2} + bx + c\). Now we can learn how to multiply a binomial and a trinomial.
To find the product of a binomial and a trinomial, multiply out the brackets:
\[(A + B)(C + D + E) = A(C + D + E) + B(C + D + E)\]
This video shows some examples of multiplying a binomial and a trinomial.
Example
Question
Find the product: \((x - 1)({x}^{2} - 2x + 1)\)
Expand the bracket
\[(x - 1)({x}^{2} - 2x + 1) = x({x}^{2} - 2x + 1) - 1({x}^{2} - 2x + 1) = {x}^{3} - 2{x}^{2} + x - {x}^{2} + 2x - 1\]Simplify
\[{(x - 1)({x}^{2} - 2x + 1)} = {x}^{3} - 3{x}^{2} + 3x - 1\]
This lesson is part of:
Algebraic Expressions Overview
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