Question

Упростите выражение: 1)(a+2)(a^2-2a+4)= 2)(x+3)(x^2-3x+9)= 3)(m-q)(m^2-3x+9)= 4)(2x-y)(4x^2+2xy+y^2)= 5)(3a-2b)(9a^2+6ab+4b^2)= 6)(1+c)(1-c+c^2)=

Answer 1

1) a^3+8
2) x^3+27
3) m^3-64
4) 8x^3-y^3
5) 27a^3-8b^3
6) 1+c^3

Answer 2

1) (a+2)(a^2-2a+4) = a(a^2-2a+4) + 2(a^2-2a+4) = a^3 - 2a^2 + 4a + 2a^2 - 4a + 8 = a^3 + 8

2) (x+3)(x^2-3x+9) = x(x^2-3x+9) + 3(x^2-3x+9) = x^3 - 3x^2 + 9x + 3x^2 - 9x + 27 = x^3 + 27

3) (m-q)(m^2-3x+9) = m(m^2-3x+9) - q(m^2-3x+9) = m^3 - 3mx + 9m - qm^2 + 3qx - 9q = m^3 - qm^2 - 3mx + 3qx + 9m - 9q

4) (2x-y)(4x^2+2xy+y^2) = 2x(4x^2+2xy+y^2) - y(4x^2+2xy+y^2) = 8x^3 + 4x^2y + 2xy^2 - 4x^2y - 2xy^2 - y^3 = 8x^3 - y^3

5) (3a-2b)(9a^2+6ab+4b^2) = 3a(9a^2+6ab+4b^2) - 2b(9a^2+6ab+4b^2) = 27a^3 + 18a^2b + 12ab^2 - 18a^2b - 12ab^2 - 8b^3 = 27a^3 - 8b^3

6) (1+c)(1-c+c^2) = 1(1-c+c^2) + c(1-c+c^2) = 1 - c + c^2 + c - c^2 + c^3 = 1 + c^3