Question

How do you find the product of (x – 4)(x – 9)?

Answer 1

Hint: In this question, we have to perform multiplication of polynomials. We will apply the distributive law of multiplication in order to obtain the solution. We should also know the various types of polynomials before performing multiplication.

Complete step by step answer:
Now, let’s solve the question.
When we talk about more than one term in an expression, we call it a polynomial.
 There are various types of polynomials.
The first one is the monomial. It is a polynomial that contains only a single term. Examples of monomials are: 4x, 2xy, 74z, etc. The second type is the binomial. As the name suggests, it contains two terms. Examples of binomials are: 2x + 6y, 4x + 1, 5xy + 8z etc. The third type is the trinomial. It is a polynomial that 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 what the distributive law of multiplication is! This law is very easy to understand.
 It is basically the way of multiplying 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 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) $
Which results in:
 $ \Rightarrow am+an+bm+bn $
Now, let’s write the expression given in question.
 $ \Rightarrow \left( x-4 \right)\left( x-9 \right) $
Now, apply the distributive law of multiplication to the above expression. We get:
 $ \Rightarrow x\times \left( x-9 \right)-4\times \left( x-9 \right) $
Now, open the brackets and solve further:
 $ \Rightarrow {{x}^{2}}-9x-4x+36 $
The next step is to solve the like terms. We get:
 $ \Rightarrow {{x}^{2}}-13x+36 $
So, we got all the unlike terms now.
This is our final answer.

Note:
Students should remember to solve all the like terms till they get all the terms unlike. It helps in reducing the expected number of terms in the product. Always try to write the terms in decreasing order of their exponent. And please do take care of the rules of integers while opening brackets.