Question

write an expression with powers to determine the difference between the surface areas of the two cubes. then, solve.

Explanation:

Step1: Recall surface - area formula for a cube

The surface - area formula of a cube is $S = 6s^{2}$, where $s$ is the side - length of the cube.

Step2: Calculate surface area of the first cube

For the cube with side - length $s_1=10$ mm, its surface area $S_1 = 6\times10^{2}=6\times100 = 600$ mm².

Step3: Calculate surface area of the second cube

For the cube with side - length $s_2 = 6$ mm, its surface area $S_2=6\times6^{2}=6\times36 = 216$ mm².

Step4: Find the difference between the two surface areas

The difference $\Delta S=S_1 - S_2=6\times10^{2}-6\times6^{2}=6(10^{2}-6^{2})$.
We know that $a^{2}-b^{2}=(a + b)(a - b)$, so $10^{2}-6^{2}=(10 + 6)(10 - 6)=16\times4 = 64$. Then $\Delta S=6\times64 = 384$ mm².

Answer:

384 mm²