To solve and simplify the expression [tex]\( 34ax^2 + 51a^2y - 68ay^2 \)[/tex], follow these steps:
1. Identify and Group Like Terms: Group the terms based on their structures. In this case, you notice that each term involves the variable [tex]\(a\)[/tex] as a common factor.
- [tex]\(34ax^2\)[/tex]
- [tex]\(51a^2y\)[/tex]
- [tex]\(-68ay^2\)[/tex]
2. Factor Out the Common Term [tex]\(a\)[/tex]: Notice that [tex]\(a\)[/tex] is a common factor in all terms of the expression.
- When you factor out [tex]\(a\)[/tex], you get:
[tex]\[
a(34x^2 + 51ay - 68y^2)
\][/tex]
3. Expression after Factoring:
- Now, our expression is [tex]\( a(34x^2 + 51ay - 68y^2) \)[/tex].
4. Verify and Simplify: To ensure the accuracy and simplicity, look at the remaining polynomial inside the parentheses.
- The resulting form inside parentheses doesn't offer any more straightforward factorizations or common terms. So, this is as simplified as the original terms could be with the given polynomial structure.
So the simplified and factored form of the given expression [tex]\(34ax^2 + 51a^2y - 68ay^2\)[/tex] is:
[tex]\[
51a^2 y + 34ax^2 - 68ay^2
\][/tex]
In this solution, we factored out the common term [tex]\( a \)[/tex] and expressed the polynomial in simplified form as [tex]\( 51a^2 y + 34ax^2 - 68ay^2 \)[/tex].
