(7𝑥−1)(−3𝑥+2)+(2𝑥+6)(8𝑥−9)

To simplify the expression \((7x - 1)(-3x + 2) + (2x + 6)(8x - 9)\), follow these steps:

### Step 1: Distribute the terms in each product.
1. For \((7x - 1)(-3x + 2)\):
   \[
   7x \cdot (-3x) + 7x \cdot 2 - 1 \cdot (-3x) - 1 \cdot 2 = -21x^2 + 14x + 3x - 2
   \]
   Simplify:
   \[
   -21x^2 + 17x - 2
   \]

2. For \((2x + 6)(8x - 9)\):
   \[
   2x \cdot 8x + 2x \cdot (-9) + 6 \cdot 8x + 6 \cdot (-9) = 16x^2 - 18x + 48x - 54
   \]
   Simplify:
   \[
   16x^2 + 30x - 54
   \]

### Step 2: Add the two simplified expressions.
\[
(-21x^2 + 17x - 2) + (16x^2 + 30x - 54)
\]

### Step 3: Combine like terms.
\[
-21x^2 + 16x^2 + 17x + 30x - 2 - 54 = -5x^2 + 47x - 56
\]

### Final Answer:
\[
-5x^2 + 47x - 56
\]

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How do you factor quadratic expressions like \(ax^2 + bx + c\)?
2. What is the difference between expanding and factoring expressions?
3. How do you solve a quadratic equation using the quadratic formula?
4. How do you identify the vertex of a parabola from its equation?
5. How do you graph the quadratic function \(f(x) = -5x^2 + 47x - 56\)?

**Tip:** When simplifying algebraic expressions, always combine like terms carefully to avoid errors.

Learn how to simplify the expression (7x - 1)(-3x + 2) + (2x + 6)(8x - 9) step-by-step with detailed solutions. This problem involves algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 7-9.

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