Question

1. Раскройте скобки: а) 3x(x^4+x^2-1)б) -5a(a^2-3a-4)в) (4b^2-4b+16)*0,5bг) 2a(2a^2-8ab+b^2)д) x^2(x^5-x^3+2x-1)е) -3z(-5z^3+2z^2-z+1)

Answer 1

2. $3x( {x}^{4} + {x}^{2} - 1) = 3 {x}^{5} + 3 {x}^{3} - 3x$
3. $- 5a( {a}^{2} - 3a - 4) = - 5 {a}^{3} + 15 {a}^{2} + 20a$
4. $(4 {b}^{2} - 4b + 16) \times 0.5b = 2 {b}^{3} - {b}^{2} + 8b$
5. $2a(2 {a}^{2} - 8ab + {b}^{2} ) = 4 {a}^{3} - 16 {a}^{2} b + 2a {b}^{2}$
6. ${x}^{2} ( {x}^{5} - {x}^{3} + 2x - 1) = {x}^{7} - {x}^{5} + 2 {x}^{3} - {x}^{2}$
7. $- 3z( - 5 {z}^{3} + 2 {z}^{2} - z + 1) = 15 {z}^{4} - 6 {z}^{3} + 3 {z}^{2} - 3z$

Answer 2

а) 3x(x^4+x^2-1) = 3x * x^4 + 3x * x^2 - 3x = 3x^5 + 3x^3 - 3x

б) -5a(a^2-3a-4) = -5a * a^2 + 15a^2 - 20a = -5a^3 + 15a^2 - 20a

в) (4b^2-4b+16)*0,5b = 4b^2 * 0,5b - 4b * 0,5b + 16 * 0,5b = 2b^3 - 2b^2 + 8b

г) 2a(2a^2-8ab+b^2) = 2a * 2a^2 + 2a * (-8ab) + 2a * b^2 = 4a^3 - 16a^2b + 2ab^2

д) x^2(x^5-x^3+2x-1) = x^2 * x^5 - x^2 * x^3 + x^2 * 2x - x^2 = x^7 - x^5 + 2x^3 - x^2

е) -3z(-5z^3+2z^2-z+1) = -3z * -5z^3 + (-3z) * 2z^2 + (-3z) * (-z) + (-3z) * 1 = 15z^4 - 6z^3 + 3z^2 - 3z