Question

How do you multiply (x – 2)(x – 3) ?

Answer 1

Hint: Here in this question, we have to perform multiplication for polynomials. We need to apply the distributive law of multiplication in which each term gets multiplied with another term. We should also know the various types of polynomials before applying distributive law. The rules of integers are also used.

Complete step by step answer:
Now, let’s solve the question.
When we write more than one term in an expression, we call it a polynomial.
As we know there are various types of polynomials.
So, the first one is a monomial which is a polynomial containing only a single term. Examples of monomials are: 4x, 2xy, 74z etc. Second one is binomial. ‘Bi’ means two and it contains two terms. Examples of binomials are: 2x + 6y, 4x + 1, 5xy + 8z etc. Third one is trinomial which is a polynomial which contains exactly three terms in an expression. Examples of trinomial are: 3x + 2y + 6z, $3{{x}^{2}}+4{{y}^{2}}+3{{z}^{2}}$, etc.
Now, let’s discuss the distributive law of multiplication. This law is too easy to understand.
According to this law, we multiply more than two terms in a systematic way such that each term gets multiplied with the other terms and no term should be left without being multiplied.
The distributive law is:
Let a, b, m, n are 4 terms.
So, if $\left( a+b \right)\times \left( m+n \right)$
Then,
$\Rightarrow a\times \left( m+n \right)+b\times \left( m+n \right)$
After multiplication it will be:
$\Rightarrow am+an+bm+bn$
Now, let’s write the expression given in question.
$\Rightarrow $(x – 2)(x – 3)
Now, we will apply the distributive law of multiplication on above expression. We will get:
$\Rightarrow x\times \left( x-3 \right)-2\times \left( x-3 \right)$
Solve further by opening the brackets:
$\Rightarrow {{x}^{2}}-3x-2x+6$
Solve the like terms in above expression:
$\Rightarrow {{x}^{2}}-5x+6$
Finally we got all the unlike terms. This becomes the final answer.

Note:
Students have to solve all the like terms till they get all the unlike terms. It will help you in reducing the expected number of terms in the solution. And always try to write the terms in decreasing order of their exponent which makes it easy to understand the solution. You have to take care of the rules of integers as well while opening brackets.