Question

How do you FOIL $\left( {2x + 3} \right)\left( {x - 2} \right)$?

Answer 1

Hint: Here we just need to multiply the two terms given in two fractions which are given in two brackets. So first we need to multiply the first elements of both brackets then both the outer digits and then inner and then at last we multiply the last digits of both the brackets. Therefore we call it FOIL which means First outer inner last.

Complete step by step solution:
Here we are given the term and we need to open the brackets by multiplying the two terms given as $\left( {2x + 3} \right)\left( {x - 2} \right)$.
So we must know what FOIL means. Whenever we have the two brackets and of the form $\left( {a + b} \right)\left( {c + d} \right)$ we multiply firstly the first elements of two brackets which are $a{\text{ and }}c$ and we get $ac$ then we have the two outer elements as $a{\text{ and }}d$ we multiply them first and get $ad$.
Now we multiply inner elements of both terms and we get $bc$ and at last the last elements of both the brackets and we get $bd$.
So we get FOIL as the First outer inner last as per the multiplication order. Now we at last need to add all the terms we have got. So we will get $ac + ad + bc + bd$.
Now we are given the term which is $\left( {2x + 3} \right)\left( {x - 2} \right)$
So multiplying the first elements we get $2x.x = 2{x^2}$
Now multiplying the outer elements we get $\left( {2x} \right)\left( { - 2} \right) = - 4x$
Now the inner elements we get $\left( 3 \right)\left( x \right) = 3x$
Now at last we multiply the last elements we get $\left( 3 \right)\left( { - 2} \right) = - 6$
Now adding all we get the result as $2{x^2} - 4x + 3x - 6$
Now we can add the two terms with the coefficient of $x$
So we get $2{x^2} - 4x + 3x - 6 = 2{x^2} - x - 6$

Hence we get that $\left( {2x + 3} \right)\left( {x - 2} \right) = 2{x^2} - x - 6$

Note:
Here the student must know what FOIL means and how to apply according to its full form. Hence it becomes easier to expand the two brackets containing two terms by applying this formula.