Question

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

binomials.


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

8x ² - 2

Answer 1

To correct the error the student made when multiplying two binomials, they need to apply the distributive property and multiply all the terms in each binomial using the FOIL method.

Step-by-step explanation:

The error the student made when multiplying the two binomials (2x + 2) and (4x - 1) is that they only multiplied the first terms, which resulted in 8x². They did not apply the distributive property to multiply all the terms in each binomial.

To correct this error, we need to multiply each term in the first binomial by each term in the second binomial. This can be done using the FOIL method, which stands for First, Outer, Inner, Last.

When we apply the FOIL method, we get the correct result: (2x + 2) (4x - 1) = 8x² + 8x - 2x - 2 = 8x² + 6x - 2.

Answer 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