MATH SOLVE

4 months ago

Q:
# which expression is a sum of cubes?A. -27a^3b^6+8a^9b^12B. -9a^3b^6+a^9b^10C. 9a^3b^6+8a^9b^12D. 27a^3b^6+8a^9b^12

Accepted Solution

A:

Answer:A. [tex]-27a^3b^6+8a^9b^{12}[/tex]D. [tex]27a^3b^6+8a^9b^{12}[/tex]

Step-by-step explanation:A. [tex]-27a^3b^6+8a^9b^{12}[/tex]which is equivalent to

[tex](-3)^3a^3(b^2)^3+2^3(a^3)^3(b^4)^3\\=(-3ab^2)^3+(2a^3b^4)^3[/tex]This expression is a sum of cubes.B. [tex]-9a^3b^6+a^9b^{10}[/tex]Here 9 is not a perfect cube and power of b in second term is 10 which is not a multiple of 3 , thus this cannot be written as sum of cubes.C. [tex]9a^3b^6+8a^9b^{12}[/tex]Here 9 is not a perfect cube. Thus this cannot be written as sum of cubes.

D. [tex]27a^3b^6+8a^9b^{12}\\=3^3a^3(b^2)^3+2^3(a^3)^3(b^4)^3\\=(3ab^2)^3+(2a^3b^4)^3[/tex]This expression is a sum of cubes.

Step-by-step explanation:A. [tex]-27a^3b^6+8a^9b^{12}[/tex]which is equivalent to

[tex](-3)^3a^3(b^2)^3+2^3(a^3)^3(b^4)^3\\=(-3ab^2)^3+(2a^3b^4)^3[/tex]This expression is a sum of cubes.B. [tex]-9a^3b^6+a^9b^{10}[/tex]Here 9 is not a perfect cube and power of b in second term is 10 which is not a multiple of 3 , thus this cannot be written as sum of cubes.C. [tex]9a^3b^6+8a^9b^{12}[/tex]Here 9 is not a perfect cube. Thus this cannot be written as sum of cubes.

D. [tex]27a^3b^6+8a^9b^{12}\\=3^3a^3(b^2)^3+2^3(a^3)^3(b^4)^3\\=(3ab^2)^3+(2a^3b^4)^3[/tex]This expression is a sum of cubes.