How do you simplify $\left( 8x+3 \right)\left( 2x+4 \right)$ ?

Hint: Here we have been asked to simplify the given expression $\left( 8x+3 \right)\left( 2x+4 \right)$ . For that we will use simple basic arithmetic calculations and reduce the expression. Initially we will multiply the both expressions after that we will have $\left( 8x+3 \right)\left( 2x+4 \right)=16{{x}^{2}}+32x+6x+12$ .

Complete step by step solution:
Now considering from the question we need to simplify the given expression $\left( 8x+3 \right)\left( 2x+4 \right)$ .
For that sake we will use simple basic arithmetic calculations like multiplication and addition.
Firstly we will perform multiplication between the expressions given in the question. After performing the multiplication we will have $\Rightarrow \left( 8x+3 \right)\left( 2x+4 \right)=16{{x}^{2}}+32x+6x+12$ .
Now we will perform the basic arithmetic addition between the similar terms in the expression $\Rightarrow 16{{x}^{2}}+32x+6x+12=16{{x}^{2}}+38x+12$ .
Now we can come to a conclusion as we observe that the given expression cannot be further simplified.
Therefore we can conclude that the simplified form of the given expression is given as
$\left( 8x+3 \right)\left( 2x+4 \right)=16{{x}^{2}}+38x+12$ .

Note: While answering questions of this type we should be sure with our calculations and concepts. We know that for any quadratic expression in the form of $a{{x}^{2}}+bx+c=0$ the roots of the expression will be given by the formulae $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ and if we assume ${{x}_{1}},{{x}_{2}}$ as two roots of the expression then the expression can be factorised as $\left( x-{{x}_{1}} \right)\left( x-{{x}_{2}} \right)=0$ and the nature of this roots is described by the discriminant value given by ${{b}^{2}}-4ac$ . For the given expression $\left( 8x+3 \right)\left( 2x+4 \right)=16{{x}^{2}}+38x+12$ the roots will be $\dfrac{-3}{8},\dfrac{-4}{2}=\dfrac{-3}{8},-2$ and the value of the discriminant will be ${{38}^{2}}-4\left( 16 \right)\left( 12 \right)=676={{26}^{2}}$ as it is greater than zero and a perfect square we will have two distinct, real roots.