Question

упростите выраженияa) (6m^2-4m+9n)(-1/6m^2) b) 2a(a-b)-a(a-2b) d)(1+3a-a^4)×5a c)2/7x(1,4x^2-3,5y) e)-1/3c^2(1,2d^2-6c) a)-0,5x^2(2x^2+6x-7) b)-x(x^2-7)+x^2(x-3) d)3a^4x(a^2-2ax+x^3-1) e)1/2ab(2/3a^2-3/4ab+4/5b^2) c)-2/5a^2y^5(5ay^2-1/2a^2b-5/6a^3)​

Answer 1

$a)(6m^2-4m+9n)\cdot(-\frac{1}{6}m^2)=-6m^2\cdot\frac{1}{6}m^2-4m\cdot(-\frac{1}{6}m^2)-9n\cdot\frac{1}{6}m^2=-m^2\cdot m^2+2m\cdot\frac{1}{3}m^2-3n\cdot\frac{1}{2}m^2=-m^4+\frac{2}{3}m^3-\frac{3}{2}m^2n\\b) 2a(a-b)-a(a-2b)=2a^2-2ab-a^2+2ab=a^2\\c)\frac{2}{7}\cdot(1,4x^2-3,5y)=\frac{2}{7}\cdot(\frac{7}{5}x^2-\frac{7}{2}y)=\frac{2}{5}x^2-y=\frac{2}{5}x^2-y\\d)3a^4x(a^2-2ax+x^3-1)=3a^4xa^2-3a^4x\cdot2ax+3a^4x\cdot x^3-3a^4x=3a^6x-6a^5x^2+3a^4x^4-3a^4x$

$e)\frac{1}{2}ab\cdot(\frac{2}{3}a^2-\frac{3}{4}ab+\frac{4}{5}b^2)=\frac{1}{2}ab\cdot \frac{2}{3}a^2-\frac{1}{2}ab\cdot\frac{3}{4}ab+\frac{1}{2}ab\cdot\frac{4}{5}b^2=ab\cdot\frac{1}{3}a^2-\frac{3}{8}a^2b^2+ab\cdot \frac{2}{5}b^2=\frac{1}{3}a^3b-\frac{3}{8}a^2b^2+\frac{2}{5}ab^3\\f)-\frac{2}{5}a^2y^5\cdot5(5ay^2-\frac{1}{2}a^2b-\frac{5}{6}a^3)=-2a^2y^5\cdot(5ay^2-\frac{1}{2}a^2b-\frac{5}{6}a^3)=-10a^3y^7+a^4by^5+\frac{5}{3}a^5y^5$

Answer 2

a) (6m^2-4m+9n)(-1/6m^2) Simplifying the expression: = (-1/6m^2)(6m^2-4m+9n) = (-1/6) + (2/3m) - (3/2n)

b) 2a(a-b)-a(a-2b) Expanding and simplifying the expression: = 2a^2 - 2ab - a^2 + 2ab = a^2

c) (1+3a-a^4)×5a Expanding and simplifying the expression: = 5a + 15a^2 - 5a^5

d) 2/7x(1.4x^2-3.5y) Simplifying the expression: = (2/7)x(1.4x^2 - 3.5y) = 0.4x^3 - x(1/2)y

e) -1/3c^2(1.2d^2-6c) Simplifying the expression: = (-1/3c^2)(1.2d^2 - 6c) = -0.4d^2/c^2 + 2/c

a) -0.5x^2(2x^2+6x-7) Expanding and simplifying the expression: = -x^4 - 3x^3 + 3.5x^2

b) -x(x^2-7)+x^2(x-3) Expanding and simplifying the expression: = -x^3 + 7x + x^3 - 3x^2 = -3x^2 + 7x

d) 3a^4x(a^2-2ax+x^3-1) Expanding and simplifying the expression: = 3a^6x - 6a^5x^2 + 3a^4x^4 - 3a^4x

e) 1/2ab(2/3a^2-3/4ab+4/5b^2) Simplifying the expression: = (1/2ab)(2/3a^2 - 3/4ab + 4/5b^2) = (1/3a) - (3/8b) + (2/5a^2b)

c) -2/5a^2y^5(5ay^2-1/2a^2b-5/6a^3) Simplifying the expression: = (-2/5a^2y^5)(5ay^2 - 1/2a^2b - 5/6a^3) = -2ay^7 + 1/5ab^2y^5 + 1/3a^4y^5