Question

Find the product $\left( x+2 \right)$ and $\left( x+3 \right)$

Answer 1

Hint: First look at definition of distributive law. Apply this to terms in the bracket. Expand the terms. By this you can derive a quadratic equation. This quadratic equation is the required result of this question.

Complete step-by-step answer:
Give product in question, which we need to solve is:
$\left( x+2 \right)$,$\left( x+3 \right)$
The product of above terms, can be written in form of :
$\left( x+2 \right)$$\left( x+3 \right)$
Let us assume this product to be denoted by P.
We can write an equation with P equal to product as:
$P=\left( x+2 \right)\left( x+3 \right)$
Distributive law:- In mathematics, distributive property of binary operations generalize the distributive law from Boolean algebra and elementary algebra. In propositional logic, distribution refers to two valid rules of replacement. Thus rule allows one to reformulate questions.
Mathematically we can write the law in the form of:
$a\left( b+c \right)=ab+ac$
Let us assume the term $\left( x+2 \right)$to be denoted by m. we can write an equation with m equal to term as:
$m=x+2$
By substituting this into equation of P, we can write it as:
$P=m\left( x+3 \right)$
By applying distributive law to above equation, we write it as:
$P=mx+3m$
By substituting value of m back into equation, we get:
$P=x\left( x+2 \right)+3\left( x+2 \right)$
By simplifying the terms, we can write the P as:
$P={{x}^{2}}+2x+3\left( x+2 \right)$
By applying distributive law to second product, we get:
$P={{x}^{2}}+2x+3.x+\left( 3 \right)*\left( 2 \right)$
By simplifying the above equation, we can write it as:
$P={{x}^{2}}+2x+3x+6$
By taking x common from middle terms, we get it as:
$P={{x}^{2}}+\left( 2+3 \right)x+6$
By simplifying, we can write it in the form of:
$P={{x}^{2}}+5x+6$
By substituting value of P, we get the equation as:
$\left( x-3 \right)\left( x+2 \right)={{x}^{2}}+5x+6$ .
Therefore this quadratic is the product of given terms.

Note: Be careful with signs while applying distributive law, because even small mistakes in sign whole answers might go wrong. At least while taking x common in the middle terms, be careful that you add the numbers correctly as it is the term that defines the equation.