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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

3 answers

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
are you sure

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!