a) if y = 6            y (y ー 9) + y      (y + 9) =

Given \( y = 6 \), let's simplify the expression step by step:

The expression is:

\[
y(y - 9) + y(y + 9)
\]

1. Substitute \( y = 6 \) into the expression:
\[
6(6 - 9) + 6(6 + 9)
\]

2. Simplify inside the parentheses:
\[
6(-3) + 6(15)
\]

3. Perform the multiplication:
\[
-18 + 90
\]

4. Finally, add the results:
\[
-18 + 90 = 72
\]

Thus, the simplified value of the expression is \( 72 \).

Would you like more details on how this was done, or do you have any questions?

Here are 5 related questions to expand on this:

1. How would the result change if \( y = -6 \)?
2. What is the general form of \( y(y - 9) + y(y + 9) \) before substituting values?
3. How do you factor expressions like \( y(y - 9) + y(y + 9) \)?
4. What is the significance of expanding and simplifying algebraic expressions?
5. How can similar expressions be used in solving quadratic equations?

**Tip**: When simplifying algebraic expressions, always follow the order of operations carefully (parentheses, exponents, multiplication/division, addition/subtraction).

Learn how to simplify the algebraic expression y(y - 9) + y(y + 9) with a step-by-step solution. This example covers core algebraic concepts such as polynomial expansion, simplification, and the difference of squares theorem. Ideal for students in Grades 8-10.

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