Question

Find the product of $(3x + 2)$ and $(4x - 3)$

Answer 1

Hint: Here we are asked to find the product of two linear algebraic equations. We first need to take the first term from the first expression and multiply it with the first term of the second expression then multiply it with the second term and add it along with its sign. These steps are repeated for all other terms in the first expression and then simplified to get the required answer.

Complete step by step solution:
Since the product of the two values means, which is the process of using the multiplication operation only. Hence the multiplication of the $(3x + 2)$ and $(4x - 3)$ is the requirement
Let $(3x + 2) \times (4x - 3)$ is the expression of the given question.
Applying the multiplication, we get $(3x + 2) \times (4x - 3) \Rightarrow (3x \times 4x) - (3x \times 3) + (2 \times 4x) - (2 \times 3)$
Thus, we have $(12{x^2}) - (9x) + (8x) - (6)$
Now let us group the like terms to simplify them and using the addition and subtraction we get $(12{x^2}) - (9x) + (8x) - (6) = 12{x^2} - x - 6$
Now we got the required answer as a quadratic equation.
Thus, product of $(3x + 2)$ and $(4x - 3)$ is $12{x^2} - x - 6$

Additional information:
In this problem we have seen how to multiply two algebraic equations if we are asked to find the sum or the difference of these two algebraic equations the below method is used.
The addition of $(3x + 2)$ and $(4x - 3)$ is $(3x + 2) + (4x - 3) = 7x - 1$
The subtraction of $(3x + 2)$ and $(4x - 3)$ is $(3x + 2) - (4x - 3) = 3x + 2 - 4x + 3 = - x + 5$

Note: In the above problem, we need to know some things to do the simplification after doing the multiplication that is grouping of like terms. The like terms are nothing but the terms having the same unknown variables. In simplifying algebraic expressions like terms are only allowed to be grouped and simplified so here in the above problem like terms are the term having the variable $x$ , so they are grouped to simplify.