Question

Match each algebraic expression to its equivalent expression. (4 points)
4x(x-5)=
(x+1)(x-1)=
2x(5x+7)=
(x+2)(x-8)=
draggables
1. x^2-6x-16
2. 4x^2-20x
3. 10x^+14x
4. x^2-1

Answer 1

are you sure

Answer 2

Let's simplify each algebraic expression one by one and match them with the given equivalent expressions.

1. **4x(x-5)**:
- Distributing \(4x\):
\[
4x \cdot x - 4x \cdot 5 = 4x^2 - 20x
\]
- Matching: **2. 4x^2 - 20x**

2. **(x+1)(x-1)**:
- Using the difference of squares:
\[
(x)^2 - (1)^2 = x^2 - 1
\]
- Matching: **4. x^2 - 1**

3. **2x(5x+7)**:
- Distributing \(2x\):
\[
2x \cdot 5x + 2x \cdot 7 = 10x^2 + 14x
\]
- Matching: **3. 10x^2 + 14x**

4. **(x+2)(x-8)**:
- Distributing:
\[
x \cdot x + x \cdot (-8) + 2 \cdot x + 2 \cdot (-8) = x^2 - 8x + 2x - 16 = x^2 - 6x - 16
\]
- Matching: **1. x^2 - 6x - 16**

Based on the simplifications, the matched expressions are:

- **4x(x-5)** = **2. 4x^2 - 20x**
- **(x+1)(x-1)** = **4. x^2 - 1**
- **2x(5x+7)** = **3. 10x^2 + 14x**
- **(x+2)(x-8)** = **1. x^2 - 6x - 16**

Answer 3

Let's double-check each expression step by step to ensure accuracy in each matching:

1. **4x(x-5)**:
- Distributing \(4x\) gives:
\[
4x \cdot x - 4x \cdot 5 = 4x^2 - 20x
\]
- This matches with **2. 4x^2 - 20x**.

2. **(x+1)(x-1)**:
- This is a difference of squares:
\[
x^2 - 1^2 = x^2 - 1
\]
- This matches with **4. x^2 - 1**.

3. **2x(5x+7)**:
- Distributing \(2x\):
\[
2x \cdot 5x + 2x \cdot 7 = 10x^2 + 14x
\]
- This matches with **3. 10x^2 + 14x**.

4. **(x+2)(x-8)**:
- Distributing:
\[
x^2 + x(-8) + 2x + 2(-8) = x^2 - 8x + 2x - 16 = x^2 - 6x - 16
\]
- This matches with **1. x^2 - 6x - 16**.

So, confirming:

- **4x(x-5)** = **2. 4x^2 - 20x**
- **(x+1)(x-1)** = **4. x^2 - 1**
- **2x(5x+7)** = **3. 10x^2 + 14x**
- **(x+2)(x-8)** = **1. x^2 - 6x - 16**

The matches are correct. Thank you for your patience!