Question

How do you simplify $\left( {x - 8} \right)\left( {x + 5} \right)$ ?

Answer 1

Hint:
To simplify these polynomials we should follow the FOIL method. Where F stands for “first terms of each binomial” , O stands for “outer terms that is first term of first binomial and last term of the last binomial” , I stands for “inner terms that is between numbers of the two binomials” and L stands for “last terms of the each binomial”.

Complete step by step solution:
The objective of the problem is to simplify $\left( {x - 8} \right)\left( {x + 5} \right)$
Given binomials $\left( {x - 8} \right)\left( {x + 5} \right)$
About polynomials : A polynomial is an algebraic expression whose power must be a non integer. A polynomial with one term is called monomial. A polynomial with two terms is called binomial and the polynomial with three terms is called trinomial.
Since given have only one term . Those are the binomials.
To simplify two binomials that is to multiply two binomials we should follow the FOIL method.
FOIL method : first multiply the first terms of each binomial and then multiply outer terms that is first term of first binomial and last term of the last binomial and then multiply inner terms that is between numbers of the two binomials and multiply last terms of the each binomial. Finally add all these terms together.
Now multiplying the first terms of each binomial that is
$x\left( x \right) = {x^2}$
On multiplying outer terms that is first term of first binomial and last term of the last binomial we get
$x\left( 5 \right) = 5x$
Then multiplying inner terms that is between numbers of the two binomials , we get
$\left( { - 8} \right)\left( x \right) = - 8x$
multiply last terms of the each binomial we get ,
$\left( { - 8} \right)\left( 5 \right) = - 40$

Finally adding all the terms we get
${x^2} + 5x - 8x - 40$
On simplifying the above equation we get ${x^2} - 3x - 40$

Thus , on simplifying $\left( {x - 8} \right)\left( {x + 5} \right)$ the result is ${x^2} - 3x - 40$

Note:
On solving these types of questions one should be careful about the signs that are plus and minus. If the both signs are equal then the resultant sign will be positive and if both the signs are different then the resultant sign will be negative.