Error Analysis - Describe and correct the error a student made when multiplying two binomials.

(2x + 2) (4x - 1)

8x ² - 2

The correct answer is:

Error made: The student multiplied only corresponding terms in each bracket with each other

Correction: Each term in one bracket is to be multiplied with every term in the next bracket

Step-by-step explanation:

The student paired the terms in the brackets into like terms and multiplied the like terms like this:

(2x + 2) × (4x - 1)  

collecting like terms: (2x, 4x) (2, -1)

(2x × 4x) (2 × (-1)) = 8x² - 2.

The above is the wrong way of expanding the bracket. The correct way of doing it is as follows:

(2x + 2) (4x - 1)

Each term in one bracket multiplies each term in the second bracket.

= 2x (4x - 1) + 2(4x -1)

= 8x² - 2x + 8x - 2

= 8x² + 6x - 2

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