Question

question 27
choose the correct words to fill in the blanks below.
sum difference cubes factored

1. the sum of two \boxed{} is given by $a^3 + b^3 = (a + b)\left(a^2 - ab + b^2\

ight)$.

1. the \boxed{} of two cubes is given by $a^3 - b^3 = (a - b)\left(a^2 + ab + b^2\

ight)$.

1. the sum of two cubes can be \boxed{}, whereas the sum of two squares cannot.
2. the expression $27 + x^6$ is an example of a \boxed{} of two cubes $3^3 + \left(x^2\

ight)^3$.
question help: message instructor

Explanation:

1. The formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ defines the sum of two cubes, so the blank matches "cubes".
2. The formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ defines the difference of two cubes, so the blank matches "difference".
3. The sum of two cubes can be rewritten into a product form (factored), while the sum of two squares cannot be factored over real numbers, so the blank matches "factored".
4. The expression $27 + x^6 = 3^3 + (x^2)^3$ is the sum of two cubes, so the blank matches "sum".

Answer:

1. cubes
2. difference
3. factored
4. sum