Question

Sum of cubes:
(a + b)(a2 – ab + b2) = a3 + b3
Difference of cubes:
(a – b)(a2 + ab + b2) = a3 – b3
Which products result in a sum or difference of cubes? Check all that apply.

(x – 4)(x2 + 4x – 16)
(x – 1)(x2 – x + 1)
(x – 1)(x2 + x + 1)
(x + 1)( + x – 1)
(x + 4)(x2 – 4x + 16)
(x + 4)(x2 + 4x + 16)

Answer 1

(x-1)(x2+x+1). (x+4) (x2-4×+16)

Answer 2

The required answer will be (x - 1)(x² + x + 1), (x + 4)(x² - 4x + 16).

Step-by-step explanation:

(x - 4)(x² + 4x - 16)

Here, it should +16 not -16. so, the given statement is false.

(x - 1)(x² - x + 1)

Here, it should be (x + 1) not (x - 1). So, the given statement is false.

(x - 1)(x² + x + 1) = x³ - 1³

So, the above statement gives the difference of cubes.

(x + 1)(x - 1) = x² - 1²

So, the above statement gives difference of squares.

(x + 4)(x² - 4x + 16) = x³ + 4³

So, the above statement gives the sum of cubes.

(x + 4)(x² + 4x + 16)

Here, it should be (x - 4) not (x + 4). So, the given statement is false.

Hence, the required answer will be (x - 1)(x² + x + 1), (x + 4)(x² - 4x + 16).