Question

Which product will result in a sum or difference of cubes?

O (x + 7)(x2 – 7x + 14)
O (X + 8)(x2 + 8x + 64)
O (x – 9)(x? mox +81)
O (X – 10)(x2 – 10x + 100)

Answer 1

(x – 9)(x² + 9x+81)

Explanation:

The sum of cubes of a and b is given by:

a³ + b³ = (a + b)(a² - ab + b²)

While the difference of cubes is given as:

a³ - b³ = (a - b)(a² + ab + b²)

1) (x + 7)(x² – 7x + 14) = x³ -7x² + 14x + 7x² - 49x + 98

= x³ -35x + 98

2) (X + 8)(x² + 8x + 64) = x³ + 8x² + 64x + 8x² + 64x + 512

= x³ + 16x² + 128x + 8³

3) (x – 9)(x² + 9x+81) = x³ + 9x² + 81x - 9x² - 81x - 729

= x³ - 9³

4) (X – 10)(x² – 10x + 100) = x³ - 10x² + 100x - 10x² + 100x - 1000

= x³ - 20x² + 200x - 10³