Question

How do you simplify (x – 2)(3x – 4)?

Answer 1

Hint: Here, in this question, we need to perform multiplication of polynomials. We should also know the various types of polynomials before performing multiplication. So, we will apply the distributive law of multiplication in order to obtain the final solution. Distributive law of multiplication is:
$\Rightarrow \left( a+b \right)\times \left( m+n \right)$ = $am+an+bm+bn$

Complete step by step answer:
Now, let’s discuss the question.
When we write more than one term in an expression, we call it a polynomial.
There are 3 types of polynomials. Let’s discuss them also. First type is monomial. It is a polynomial which contains only a single term. Few examples of monomials are: 4x, 2xy, 74z etc. Second one is binomial. It contains only two terms. Few examples of binomial are: 2x + 6y, 4x + 1, 5xy + 8z etc. Third type is trinomial. It is a polynomial which contains exactly three terms in an expression. Quadratic equations are also trinomials. Few examples of trinomial are: 3x + 2y + 6z, $3{{x}^{2}}+4{{y}^{2}}+3{{z}^{2}}$, etc.
So now, we will know about a law which we will be using to solve the given expression. This law is a distributive law of multiplication and it is too easy to understand.
 It is basically the way of multiplying more than two terms in such a way 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,
$\Rightarrow a\times \left( m+n \right)+b\times \left( m+n \right)$
Which will result in:
$\Rightarrow am+an+bm+bn$
Now, let’s write the expression given in question.
$\Rightarrow $(x – 2)(3x – 4)
Now, apply the distributive law of multiplication on given expression. We will get:
$\Rightarrow x\times \left( 3x-4 \right)-2\times \left( 3x-4 \right)$
Open the brackets and solve further:
$\Rightarrow 3{{x}^{2}}-4x-6x+8$
Add the like terms:
$\Rightarrow 3{{x}^{2}}-10x+8$
As we got all the unlike terms so there is no need to solve further. This is the final answer.

Note:
Students should remember to solve all the like terms till they get all the unlike terms in the final step. It also helps in reducing the expected number of terms in the final product. Do remember to try to write the terms in decreasing order of their exponent or power. While opening brackets, rules of integers must be followed.