Write an expression with five different terms that is equivalent to $8 x^{2} + 3 x^{2} + 3 y$ . Justify your answer.

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Solution

Step 1: Given expression is $8 x^{2} + 3 x^{2} + 3 y$
Simplifying the given expression to the simplest form we get
$8 x^{2} + 3 x^{2} + 3 y = (8 + 3) x^{2} + 3 y {D i s t r i b u t i v e p r o p e r t y} = (11) x^{2} + 3 y$
Step 2: Expression with five different terms
Consider $2 x^{2} + 3 x^{2} + 2 y + 1 y + 6 x^{2}$
This expression contains 5 different terms
Now after simplifying this we get:
$= 2 x^{2} + 3 x^{2} + 2 y + 1 y + 6 x^{2} = (2 + 3 + 6) x^{2} + (2 + 1) y {D i s t r i b u t i v e p r o p e r t y} = 11 x^{2} + 3 y {s i m p l e s t f o r m}$
We can see that simplest is same.
Final Answer: $2 x^{2} + 3 x^{2} + 2 y + 1 y + 6 x^{2}$

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