Question

Which expression is equivalent to 12^3 - 10^3?

a) (12 - 10)(144 + 100)
b) (12 + 10)(144 - 100)
c) (12 - 10)(144 + 120 + 100)
d) (12 + 10)(144 - 120 + 100)

Answer 1

The expression equivalent to 12^3 - 10^3 is found by factoring the difference of cubes, leading to option c) (12 - 10)(144 + 120 + 100).

Step-by-step explanation:

The student asked which expression is equivalent to 12^3 - 10^3. This can be solved by recognizing it as a difference of cubes, a^3 - b^3, which factors to (a - b)(a^2 + ab + b^2). By applying this to 12^3 - 10^3, we get:

• (12 - 10) which is 2,
• (12^2) which is 144,
• (12)(10) which is 120,
• (10^2) which is 100.

Therefore, the expression becomes (12 - 10)(144 + 120 + 100), which matches option c).