Canceling the right way

Algebra Level 2

Students often make the misconception that $a^n + b^n = (a+b)^n$ is an identity. But sometimes this equation can be true under specific scenarios.

If $a^3 + b^3 = (a+b)^3$ , then which of the following must definitely be true?

a=0

only At least one of the other choices is true

a+b=0

only

b=0

only

1 solution

Anandmay Patel
Oct 14, 2016

If $a^3+b^3=(a+b)^3$ then $a^3+b^3=a^3+b^3+3ab(a+b)$ . Equivalently,we can write: $3ab(a+b)=0$ . So any one of the $a,b$ or $(a+b)$ maybe zero in order to make $3ab(a+b)$ zero.

Canceling the right way

1 solution

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