Write as a product 27a^3−(a−b)^3

Mathematics

1 answer:

jarptica [38.1K]3 years ago

6 0

Answer:

(2a +b)·(13a^2 -5ab +b^2)

Step-by-step explanation:

The factorization of the difference of cubes is a standard form:

(p -q)^3 = (p -q)(p^2 +pq +q^2)

Here, you have ...

p = 3a
q = (a-b)

so the factorization is ...

(3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q

= (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit

= (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms

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