Question

one algebraic expression has got three terms.Another algebraic expression has got three terms.If we combine these two expressions,what is the minimum number of terms the new expression could have?Give an example for this.What is the maximum number of terms the new expression could have?Give an example

Answer 1

Dear Student,

Let P(x)=$a{x}^2-bx+c=0$
Q(x)=$bx-a{x}^2-c=0$
If both the algebraic expressions are added
we get P(x)+Q(x)
$$\begin{gathered} \Rightarrow a{x}^2-bx+c+\left(bx-a{x}^2-c\right) \\ =a{x}^2-bx+c+bx-a{x}^2-c \\ =0 \end{gathered}$$

So minimum number of terms if two algebraic expressions are added is 0.

To find maximum number of terms
Let P(x)=$a{x}^3+b{x}^2+cx=0$
Q(x)=$a{x}^5+b{x}^4+d=0$

if we add both P and Q
$a{x}^5+b{x}^4+a{x}^3+b{x}^2+cx+d=0$
Total number of terms is 6.

Hence maximum number of terms if two algebraic expressions are added is sum of terms in both expressions.

Regards,