Question

factor 8y. 27 pls answer it correctly​

Answer 1

Step-by-step explanation:

1 Answer

8y3−27

=

(2y)3−33

=

(2y−3)((2y)2+3(2y)+32)

=

(2y−3)(4y2+6y+9)

based on the difference of cubes identity:

m3−n3

=

(m−n)(m2+mn+n2)

,

with m

= 2y

and n

= 3

Note that

(

4y2+6y+9)

has no simpler factors with real coefficients. To check this, note that it is of the form

ay2+by+c

with a. =4 ,

b. = 6 and

c =9

, which has discriminant given by the formula:

Δ = b2 − 4ac. = 62− (4×4×9)

= 36 − 144 = −108 < 0

Just as a potential point of interest, if you were allowed complex coefficients, this would factor as:

(4y2+6y+9) = (2y−3ω)(2y−3ω2)

where

ω = −12+√32i

is known as the primitive cube root of unity...