Question

How do you find the product \[\left( {4x + 1} \right)\left( {6x + 3} \right)\] ?

Answer 1

Hint: We have an algebraic expression and we need to simplify this. Here we have ‘4x’ and ‘6x’ are algebraic terms. The multiplication of two or more monomial expressions or expressions with one term means finding the product of all the expressions involved. Here we have 4x meaning that 4 is a coefficient of ‘x’ and 6x means 6 is a coefficient of x.

Complete step by step solution:
Given,
 \[\left( {4x + 1} \right)\left( {6x + 3} \right)\]
That is,
 \[ \Rightarrow \left( {4x + 1} \right)\left( {6x + 3} \right)\]
Now applying the multiplying ‘4x’ with \[\left( {6x + 3} \right)\] and 1 with \[\left( {6x + 3} \right)\] . That is
 \[ \Rightarrow 4x\left( {6x + 3} \right) + 1\left( {6x + 3} \right)\]
Expanding the brackets we have,
 \[ \Rightarrow 24{x^2} + 12x + 6x + 3\]
All we did is multiply the coefficients and the variables separately. Here xa’ is the variable or unknown term.
Now adding the like terms we have
 \[ \Rightarrow 24{x^2} + 18x + 3\] .
Hence the multiplication of \[\left( {4x + 1} \right)\left( {6x + 3} \right)\] is
 \[ \Rightarrow 24{x^2} + 18x + 3\] .
So, the correct answer is “ \[ \Rightarrow 24{x^2} + 18x + 3\] ”.

Note: If we the value of ‘a’ we will have a value for the given expression. While multiplication of monomials by monomial expression the rule or equation that applies is product of their coefficients and product of the variables. The rule that applies to the multiplication of monomials and a polynomial is the distributive law. The law shows that each term of the polynomial should be individually multiplied by the monomial expression.
Here in the final result we have a quadratic equation that is a polynomial of degree 2. If we solve the quadratic equation we will have two roots or two zeros. We solve the obtained equation by factorization method or by quadratic formula method or by completing the square.