Question

Представьте в виде произведения многочленов: 1) m^3+n^3; 2) a^3+1 3) 8x^3+64 4)27m^3+8n^3 5)125x^3+216y^3

Answer 1

1) m^3+n^3=(m+n)(m²-mn+n²)

2) a^3+1=(a+1)(a²-a+1)

3) 8x^3+64=(2x+4)(4x²-8x+16)

4)27m^3+8n^3=(3m+2n)(9m²-6mn+4n²)

5)125x^3+216y^3=(5x+6y)(25x²-30xy+36y²)

Answer 2

1. m^3 + n^3 can be represented as the sum of two cubes: m^3 + n^3 = (m + n)(m^2 - mn + n^2)

2. a^3 + 1 can be represented as the sum of two cubes: a^3 + 1 = (a + 1)(a^2 - a + 1)

3. 8x^3 + 64 can be represented as the sum of two cubes: 8x^3 + 64 = 8(x^3 + 8) = 8(x + 2)(x^2 - 2x + 4)

4. 27m^3 + 8n^3 can be represented as the sum of two cubes: 27m^3 + 8n^3 = (3m)^3 + (2n)^3 = (3m + 2n)(9m^2 - 6mn + 4n^2)

5. 125x^3 + 216y^3 can be represented as the sum of two cubes: 125x^3 + 216y^3 = (5x)^3 + (6y)^3 = (5x + 6y)(25x^2 - 30xy + 36y^2)