Question

1) (0.2а+10b)³ 2) (0.3b-10c)³

Answer 1

$(0,2a+10b)^3=(0,2a)^3+3(0,2a)^2*10b+3*0,2a*(10b)^2+(10b)^3=\\=0,002a^3+1,2a^2b+60ab^2+1000b^3\\\\(0,3b-10c)^3=(0,3b)^3-3(0,3b)^2*10c+3*0,3b(10c)^2-(10c)^3=\\=0,027b^3-2,7b^2c+90bc^2-1000c^3$

Answer 2

To expand the given expressions, we can use the binomial expansion formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Let's apply this formula to each expression:

1. (0.2a + 10b)³: Using the formula, we have: (0.2a + 10b)³ = (0.2a)³ + 3(0.2a)²(10b) + 3(0.2a)(10b)² + (10b)³ = 0.008a³ + 0.12a²b + 0.6ab² + 1000b³

Therefore, the expanded form of (0.2a + 10b)³ is 0.008a³ + 0.12a²b + 0.6ab² + 1000b³.

2. (0.3b - 10c)³: Applying the formula, we get: (0.3b - 10c)³ = (0.3b)³ - 3(0.3b)²(10c) + 3(0.3b)(10c)² - (10c)³ = 0.027b³ - 0.9b²c + 9bc² - 1000c³

Hence, the expanded form of (0.3b - 10c)³ is 0.027b³ - 0.9b²c + 9bc² - 1000c³.