1. For 8m³ - 27, you can use the difference of cubes formula: a³ - b³ = (a - b)(a² + ab + b²). In this case, a is 2m, and b is 3. So, it factors as:
8m³ - 27 = (2m - 3)(4m² + 6m + 9).
2. For 64y³ + 125, you can use the sum of cubes formula: a³ + b³ = (a + b)(a² - ab + b²). In this case, a is 4y, and b is 5. So, it factors as:
64y³ + 125 = (4y + 5)(16y² - 20y + 25).
3. To factor the trinomial x² - 6x - 18, you're looking for two numbers that multiply to the constant term (-18) and add up to the coefficient of the middle term (-6). The two numbers are -9 and 2. So, you can factor it as:
Answers & Comments
Answer:
To factor the expressions you've provided:
1. For 8m³ - 27, you can use the difference of cubes formula: a³ - b³ = (a - b)(a² + ab + b²). In this case, a is 2m, and b is 3. So, it factors as:
8m³ - 27 = (2m - 3)(4m² + 6m + 9).
2. For 64y³ + 125, you can use the sum of cubes formula: a³ + b³ = (a + b)(a² - ab + b²). In this case, a is 4y, and b is 5. So, it factors as:
64y³ + 125 = (4y + 5)(16y² - 20y + 25).
3. To factor the trinomial x² - 6x - 18, you're looking for two numbers that multiply to the constant term (-18) and add up to the coefficient of the middle term (-6). The two numbers are -9 and 2. So, you can factor it as:
x² - 6x - 18 = (x - 9)(x + 2).