Multiply: (3x+4)(2x-1)6x2+5x+46x2+5x-46x2-5x+46x2-5x-4Evaluate: (2x+3)29m2+12mn+4n29m2+12mn-4n29m2-12mn-4n29m2-12mn+4n2If , what is x?2348Which is NOT a real-world application of exponential equations?Population growthSolving quadratic equationsRadioactive decayCompound interestIf 2y2-10y+12=0, which of these is the set of value of y?{-2,-3}{2,-3}{-2,3}{2,3}The expression ax2+bx+C =0 is called Quartic equationLinear equation=Quadratic Equation Quadratic Function Factorize the expression 5m2n-10mn2+mnmn(5m-10n+1)mn(5m-10n-1)mn(5m+10n-1)mn(5m+10n+1)solve the equation using quadratic formula: x2-4x+3=0(3 & 1)(-3 & -1)(3 & -1)(-3 & 1)

Let's break down and solve each question.

### 1. **Multiply: \((3x+4)(2x-1)\)**
   \[
   (3x+4)(2x-1) = 3x(2x) + 3x(-1) + 4(2x) + 4(-1) = 6x^2 - 3x + 8x - 4 = 6x^2 + 5x - 4
   \]
   Simplified result: \(6x^2 + 5x - 4\)

### 2. **Evaluate: \((2x+3)^2\)**
   \[
   (2x+3)^2 = (2x+3)(2x+3) = 2x(2x) + 2x(3) + 3(2x) + 3(3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9
   \]
   Simplified result: \(4x^2 + 12x + 9\)

### 3. **Evaluate: \(9m^2 + 12mn + 4n^2\)**
   This expression is already simplified, so the evaluated result is the same:
   Simplified result: \(9m^2 + 12mn + 4n^2\)

### 4. **If \(2x = 4\), what is \(x\)?**
   Solve for \(x\):
   \[
   2x = 4 \implies x = \frac{4}{2} = 2
   \]
   Value of \(x\): \(x = 2\)

### 5. **Which is NOT a real-world application of exponential equations?**
   - Population growth
   - **Solving quadratic equations** (Correct Answer)
   - Radioactive decay
   - Compound interest
   
   Explanation: Solving quadratic equations is not an application of exponential equations; instead, it's related to polynomial equations.

### 6. **If \(2y^2 - 10y + 12 = 0\), which of these is the set of values of \(y\)?**
   Solve using the quadratic formula:
   \[
   y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   For \(2y^2 - 10y + 12 = 0\):
   - \(a = 2\)
   - \(b = -10\)
   - \(c = 12\)
   
   Discriminant:
   \[
   \Delta = (-10)^2 - 4(2)(12) = 100 - 96 = 4
   \]
   Roots:
   \[
   y = \frac{10 \pm \sqrt{4}}{4} = \frac{10 \pm 2}{4}
   \]
   \[
   y = \frac{12}{4} = 3 \quad \text{or} \quad y = \frac{8}{4} = 2
   \]
   Set of values: \(\{2, 3\}\)

### 7. **The expression \(ax^2 + bx + c = 0\) is called:**
   - **Quadratic Equation** (Correct Answer)
   
   Explanation: This is the standard form of a quadratic equation.

### 8. **Factorize the expression \(5m^2n - 10mn^2 + mn\):**
   Factor out the common term \(mn\):
   \[
   mn(5m - 10n + 1)
   \]
   Correct factorization: \(mn(5m - 10n + 1)\)

### 9. **Solve the equation using quadratic formula: \(x^2 - 4x + 3 = 0\):**
   Use the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   For \(x^2 - 4x + 3 = 0\):
   - \(a = 1\)
   - \(b = -4\)
   - \(c = 3\)
   
   Discriminant:
   \[
   \Delta = (-4)^2 - 4(1)(3) = 16 - 12 = 4
   \]
   Roots:
   \[
   x = \frac{4 \pm \sqrt{4}}{2} = \frac{4 \pm 2}{2}
   \]
   \[
   x = \frac{6}{2} = 3 \quad \text{or} \quad x = \frac{2}{2} = 1
   \]
   Set of values: \(\{3, 1\}\)

### Summary:
1. Simplified multiplication: \(6x^2 + 5x - 4\)
2. Evaluated square: \(4x^2 + 12x + 9\)
3. Given polynomial: \(9m^2 + 12mn + 4n^2\)
4. \(x = 2\)
5. Non-exponential application: Solving quadratic equations
6. \(y\) values: \(\{2, 3\}\)
7. Expression type: Quadratic Equation
8. Factorized expression: \(mn(5m - 10n + 1)\)
9. Quadratic roots: \(\{3, 1\}\)

Would you like more details or have any questions? Here are five related questions to consider:
1. What is the significance of the discriminant in quadratic equations?
2. How do you recognize if an equation is linear or quadratic?
3. What are some common applications of quadratic equations in real life?
4. Can you explain the process of completing the square to solve quadratic equations?
5. What happens when the discriminant of a quadratic equation is negative?

**Tip:** When factoring, always look for common factors before applying more complex methods.

Explore detailed solutions to multiplication of binomials, evaluation of polynomials, solving quadratic equations, and factorization of polynomials. Ideal for Grades 9-12 students studying algebra and quadratic equations.

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