Question

B. 64x3 - 125
Factor sum or difference of cubes

Answer 1

(4x -5)(16x^2 +20x +25)

Explanation:

The factoring of the difference of cubes is something you might want to memorize, or keep handy:

(a³ -b³) = (a -b)(a² +ab +b²)

Here, the minus sign in the middle tells you this is a difference. The power of x is a clue that this might be the difference of cubes. Your knowledge of cubes of small integers tells you ...

• 64 = 4³
• 125 = 5³

so you can recognize this as ...

(4x)³ - 5³ . . . . . the difference of cubes.

___

Since you are familiar with the factorization above, you can easily write down the factoring of this expression using a=4x, b=5.

(4x -5)(16x² +20x +25)

_____

For "completeness", here is the factorization of the sum of cubes:

a³ +b³ = (a +b)(a² -ab +b²)

Note the linear factor (a +b) has the same sign as the sign between the cubes. The sign of the middle 2nd-degree term (ab) is opposite that.