Answer:
(4x -5)(16x^2 +20x +25)
Step-by-step 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 ...
so you can recognize this as ...
(4x)³ - 5³ . . . . . the difference of cubes.
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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)
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For "completeness", here is the factorization of the <em>sum of cubes</em>:
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.
