Question

1)3a(a²-5a+1) 2)-5b(2b²-3b+2) 3)(4a³+3a²-6)·(-2a²) 4)(5x^4-4x³+2x)·(-3x³) 5)2ab·(3a²b²-2ab³+5)

Answer 1

1) 3а^3–15а^2+3а

2) –10б^3+15б^2–10б

3) –8а^5–6а^4+12а^2

4) –15х^7+12х^6–6х^4

5) 6а^3 б^3–4а^2 б^4+10аб

Answer 2

To simplify each of the given expressions, we can use the distributive property and then combine like terms. Let's solve each expression step by step:

1. 3a(a² - 5a + 1) Distribute 3a to each term inside the parentheses: 3a * a² - 3a * 5a + 3a * 1 3a³ - 15a² + 3a

2. -5b(2b² - 3b + 2) Distribute -5b to each term inside the parentheses: -5b * 2b² + 5b * 3b - 5b * 2 -10b³ + 15b² - 10b

3. (4a³ + 3a² - 6) · (-2a²) Distribute -2a² to each term inside the parentheses: -2a² * 4a³ - 2a² * 3a² - 2a² * -6 -8a⁵ - 6a⁴ + 12a²

4. (5x⁴ - 4x³ + 2x) · (-3x³) Distribute -3x³ to each term inside the parentheses: -3x³ * 5x⁴ - 3x³ * -4x³ + -3x³ * 2x -15x⁷ + 12x⁶ - 6x⁴

5. 2ab · (3a²b² - 2ab³ + 5) Distribute 2ab to each term inside the parentheses: 2ab * 3a²b² - 2ab * 2ab³ + 2ab * 5 6a³b³ - 4a²b⁴ + 10ab

So, the simplified expressions are:

1. 3a³ - 15a² + 3a
2. -10b³ + 15b² - 10b
3. -8a⁵ - 6a⁴ + 12a²
4. -15x⁷ + 12x⁶ - 6x⁴
5. 6a³b³ - 4a²b⁴ + 10ab