Question

1. Разложите на множители: 1) a³+8 2)1-p³ 3)n⁶-1 4)c³-64x³ 5)27a³+b³ нужна срочна пажалуста зарания спасиба

Answer 1

Ответ:

1)а³+8а³=а³+2³=(а+2)(а²-2а+4)

2)1-р³=1³-р³=(1-р)(1+р+р²)

3)n⁶-1=(n³-1)(n³+1)=(n-1)(n²+n+1)(n+1)(n²-n+1)

4)c³-64x³=c³-4³x³=c³-(4x)³=(c-4x)(c²+4cx+16x²)

5)27a³+b³=3³a³+b³=(3a)³+b³=(3a+b)(9a²-3ab+b²)

Answer 2

Factoring Expressions

1) a³ + 8 To factor the expression a³ + 8, we can use the formula for factoring the sum of cubes: a³ + b³ = (a + b)(a² - ab + b²). Applying this formula, we get: a³ + 8 = (a + 2)(a² - 2a + 4)

2) 1 - p³ The expression 1 - p³ can be factored using the formula for the difference of cubes: a³ - b³ = (a - b)(a² + ab + b²). Therefore: 1 - p³ = (1 - p)(1 + p + p²)

3) n⁶ - 1 The expression n⁶ - 1 can be factored as a difference of squares: a² - b² = (a - b)(a + b). Hence: n⁶ - 1 = (n³ - 1)(n³ + 1)

4) c³ - 64x³ The expression c³ - 64x³ is a difference of cubes, which can be factored using the formula: a³ - b³ = (a - b)(a² + ab + b²). Therefore: c³ - 64x³ = (c - 4x)(c² + 4cx + 16x²)

5) 27a³ + b³ The expression 27a³ + b³ is a sum of cubes, and we can use the formula: a³ + b³ = (a + b)(a² - ab + b²). Thus: 27a³ + b³ = (3a + b)(9a² - 3ab + b²)

I hope this helps! If you have any more questions or need further assistance, feel free to ask.