Question

How do you express the product $(2x - 1)(3x + 4)$ as a trinomial?

Answer 1

Hint: A Trinomial is any mathematical expression that contains three terms. Firstly, we multiply both the linear expressions since multiplication has higher precedence as per the BODMAS rule. Then we further evaluate the expression by performing operations such as subtraction and addition with the same degree terms and then constants. In the end, we get three terms as the solution.

Complete step-by-step solution:
The given expression is, $(2x - 1)(3x + 4)$
Firstly, Perform the multiplication operation since it has the highest precedence according to the BODMAS rule.
On opening the brackets, we get,
$\Rightarrow \left[ {2x(3x + 4) - 1(3x + 4)} \right]$
Now we shall firstly multiply the constant with the contents in the brackets,
$\Rightarrow \left[ {2x(3x + 4) - (3x + 4)} \right]$
Now multiply the variable to the linear expression inside the brackets.
$\Rightarrow \left[ {(6{x^2} + 8x) - (3x + 4)} \right]$
In the second half of the expression, there is a negative sign outside the brackets. Multiply it with the linear equation inside the brackets.
Finally, we get,
$\Rightarrow \left[ {6{x^2} + 8x - 3x - 4} \right]$
Now since there are two terms of the same degree, perform the respective subtraction or addition operation.
After further evaluating we get,
$\Rightarrow \left[ {6{x^2} + 5x - 4} \right]$

The product $(2x - 1)(3x + 4)$ when expressed as a trinomial we get, $6{x^2} + 5x - 4$.

Note: This is a polynomial of a degree $2$ since there is a term with power $2$ (highest of all). It is also known as a quadratic equation. The given expression in the question is the solution of the quadratic equation we got at the end. Since it is a degree $2$ polynomial, we shall have two roots.