Question

Which expression is a sum of cubes?


A) -27a^ b^6 + 8a^9 b^12

B) -9a^3 b^6 + a^9 b^10

C) 9a^3 b^6 + 8a^9 b^12

D) 27a^3 b^6 + 8a^9 b^12

Answer 1

$A) -27a^3 b^6 + 8a^9 b^{12}\\D) 27a^3 b^6 + 8a^9 b^{12}$

Step-by-step explanation:

Here, the given expressions are:

$A) -27a^3 b^6 + 8a^9 b^{12}\\= (-3)^3(a^3)(b^2)^3 + (2)^3(a^3)3(b^4)^3\\= (-3ab^2)^3 +(2a^3b^4)^3$

So, the above expression is "sum of cubes".

$B) -9a^3 b^6 + a^9 b^{10}$

But (-9) can not be expressed as a Perfect cube root.

So, the above expression is not "sum of cubes".

$C) 9a^3 b^6 + 8a^9 b^{12}$

But (9) can not be expressed as a Perfect cube root.

So, the above expression is not "sum of cubes".

$D) 27a^3 b^6 + 8a^9 b^{12}\\\\= (3)^3a^3(b^2)^3 + (2)^3(a^3)^3(b^4)^3\\= (3ab^2)^3+ (2a^3b^4)^3$

So, the above expression is  "sum of cubes".

Answer 2

Answer:

D on E2020

Step-by-step explanation: