(y + 7)/(7 * 135) * (x ^ 2 - 3x - 90)/(1 - 8)

Let's simplify the given expression step by step:

The expression is:

\[
\frac{(y + 7)}{7 \times 135} \times \frac{(x^2 - 3x - 90)}{1 - 8}
\]

### Step 1: Simplify the constants in the denominator

First, calculate the denominator:

\[
7 \times 135 = 945
\]

So the expression becomes:

\[
\frac{(y + 7)}{945} \times \frac{(x^2 - 3x - 90)}{-7}
\]

### Step 2: Multiply the two fractions

Multiply the numerators and the denominators:

\[
\frac{(y + 7) \times (x^2 - 3x - 90)}{945 \times (-7)}
\]

Simplify the denominator:

\[
945 \times (-7) = -6615
\]

So, the expression is:

\[
\frac{(y + 7) \times (x^2 - 3x - 90)}{-6615}
\]

### Final Answer

\[
\frac{(y + 7) \times (x^2 - 3x - 90)}{-6615}
\]

This is the simplified form of the given expression.

Would you like to see the detailed steps for factoring the quadratic expression or any further explanations?

Here are 5 related questions:
1. How can we factor the quadratic expression \(x^2 - 3x - 90\)?
2. What are the roots of the equation \(x^2 - 3x - 90 = 0\)?
3. How can we simplify fractions with polynomial numerators?
4. How does multiplying fractions work in algebra?
5. How do we deal with negative signs in algebraic fractions?

**Tip:** Always check for common factors between the numerator and denominator to simplify fractions further.

Learn how to simplify the algebraic expression (y + 7)/(7 * 135) * (x ^ 2 - 3x - 90)/(1 - 8) step-by-step with detailed explanations. This problem covers algebraic fraction simplification and quadratic equations, suitable for advanced high school students (Grades 10-12).

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