Question

How do you expand and simplify \[\left( {2x - 3} \right)\left( {3x + 4} \right)\]?

Answer 1

Hint: In order to expand the above expression use the order of expanding as FOIL i.e. First,Outside,Inside,Last and later for simplification combine all the like terms to get the required answer.

Complete step-by-step answer:
We are given a polynomial having one variable $ x $ in the term.
Let’s suppose the function given be $ f\left( x \right) $
 $ f\left( x \right) = \left( {2x - 3} \right)\left( {3x + 4} \right) $
First we have to expand the above equation, to expand any binomial expression there is an order by which we can expand the expression easily. You can use the acronym FOIL which means First, Outside,Inside,Last to remember the order of expansion .
 $
  f\left( x \right) = 2x\left( {3x + 4} \right) - 3\left( {3x + 4} \right) \\
   = 6{x^2} + 8x - 9x - 12 \;
  $
Now Simplification means to combine all the like term in the equation, so in our equation combine terms having $ x $
Our equation becomes
 $ f\left( x \right) = 6{x^2} + 8x - 9x - 12 $
Therefore, expansion and simplification of \[\left( {2x - 3} \right)\left( {3x + 4} \right)\]is $ 6{x^2} + 8x - 9x - 12 $
So, the correct answer is “ $ 6{x^2} + 8x - 9x - 12 $ ”.

Note: A quadratic equation is a equation which can be represented in the form of $ a{x^2} + bx + c $ where $ x $ is the unknown variable and a,b,c are the numbers known where $ a \ne 0 $ .If $ a = 0 $ then the equation will become linear equation and will no more quadratic .
The degree of the quadratic equation is of the order 2.