Question

The product of $\left( {2x + 3} \right)$ and $\left( {3x + 2} \right)$ is given by
A) $6{x^2} + 6$
B) $6{x^2} + 5x + 6$
C) $6\left( {{x^2} + x + 1} \right)$
D) $6{x^2} + 13x + 6$

Answer 1

Hint:
we are asked to find the product of two polynomials . The product of polynomials $\left( {ax + b} \right)$ and $\left( {cx + d} \right)$ is given by $ax(cx + d) + b(cx + b)$.Using this we get our product of the given polynomials.

Complete step by step solution:
We are given two polynomials $\left( {2x + 3} \right)$ and $\left( {3x + 2} \right)$ and we need to find the product of these polynomials
The product of polynomials $\left( {ax + b} \right)$ and $\left( {cx + d} \right)$ is given by
$ \Rightarrow ax(cx + d) + b(cx + b)$
So now by using this principle we can multiply our given polynomials
$ \Rightarrow 2x(3x + 2) + 3(3x + 2)$
Now multiplying we get,
$
   \Rightarrow 2x(3x + 2) + 3(3x + 2) \\
   \Rightarrow 6{x^2} + 4x + 9x + 6 \\
   \Rightarrow 6{x^2} + 13x + 6 \\
$
Therefore the product of the given polynomials is $6{x^2} + 13x + 6$.

The correct option is d.

Note:
Distribute each term of the first polynomial to every term of the second polynomial. Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents.