Знайти нулі функції y=-2x+6

Объяснение:

_1_

1) 3*(5х + 9у – z)=3*5x+3*9y-3*z=15x+27y-3z;

2) –6*(–а – 9b + 7с)=-6*(-a)-6*(-9b)-6*(7c)=6a+54b-42c;

3) (6р – n – 4m) * (–1,6)=(–1,6)*6p-(–1,6)*n-(–1,6)*4m=-9,6p+1,6n+6,4m;

4) (–2,6а – b + 1,4с) * (–m)= (–m)*(-2,6a)- (–m)*b+ (–m)*1,4c=2,6am+bm-1,4cm;

5) –0,7n*(7а – 2,1 + 5k)=(–0,7n)*7a-(–0,7n)*2,1+(–0,7n)*5k=-4,9na+1,47n=3,5nk;

_2_

1) 5х + 5у=5*(x+y);

2) 10аb + 3bc – b=b*(10a+3c-1);

3) 12mр – 16nр=4p*(3m-4n);

_3_

1) (x + 7,1) – (8,7 + х)=x + 7,1 – 8,7 - х=7,1 – 8,7= -(8,7-7,1)=-1,6;

2) –(7,3 – у) – (9,1 + у)= –7,3 + у – 9,1 - у=–7,3 – 9,1=-(7,3+9,1)=-16,4;

3) –(7,2 – m + k) + (5,3 + k)= –7,2 + m - k + 5,3 + k=–7,2 + m + 5,3 =m-(7,2-5,3)=m-1,9;

4) (b – с – 4,8) – (–с – b – 4,8)=b – с – 4,8 +с + b + 4,8=b + b =2b;

_4_

1) 7x – 18x – 19x + 21x=x(21-19-18+7)=x(9-18)=-x(18-9)=-9x;

2) –9у + 12у + 41y – 17y=y(12+41-17-9)=y(53-17-9)=27y;

3) 2,6а – 5,4b – а + 2b=a(2,6-1)-b(5,4-2)=1,6a-3,4b;

4) –5,6с + 4,8 + 8,2с – 9,1=c(8,2-5,6)-(9,1-4,8)=2,6c-4,3;

5) 4,6m + 8,3n – 5,1 – 8,3m – 6,4n=n(8,3-6,4)-m(8,3-4,6)-5,1=1,9n-3,7m-5,1;

6) –2a/3 + 5b/6 – a/8 – 7b/12=b/6(5-7/2)-a(2/3+1/8)=b/6(5-3,5)-a(2/3+1/8)=1,5b/6-19a/24=b/4-19a/24;

_5_

1) 9(7x – 6) – 18х=9*7x-9*6-18x=63x-18x-54=45x-54;

2) 7а – 6(19 – а)=7a-6*19+6*a=13a-114;

3) 0,8(6x – 2) + 1,6(х – 4)=0,8*6x-0,8*2+1,6*x-1,6*4=4,8x-1,6+1,6x-6,4=x(4,8+1,6)-(1,6+6,4)=6,4x-8;

4) 2,8(5b – 6а) – (7b – 8а) * 1,2=2,8*5b-2,8*6a-1,2*7b+1,2*8a=14b-16,8a-8,4b+9,6a=b(14-8,4)-a(16,8-9,6)=5,6b-7,2a;

5) –(–4,9 – 5,8с) – (3,1с – 5,6)=4,9 + 5,8с – 3,1с +5,6=c(5,8 – 3,1)+4,9+5,6=2,7c+10,5;

6) 8/9 * (2 1/4 * a – 3b/4) – 7/30 * (4 2/7 * a – 8 4/7 * b)=8/9 * (9/4 * a – 3b/4) – 7/30 * (30/7 * a – 60/7 * b)=2a – b*(2/3)– a + 2 b=a+b*(4/3);

_6_

6а – (3а – 9b),

а + 3b = –0,6.

6а – (3а – 9b)=6а – 3а + 9b=3a+9b=3*(a+3b)=3*(-0,6)=-1,8;

_7_

1) 0,6(4у – 18) – 0,4(5 – 7у)=2,4y-10,8-2+2,8y=5,2y-12,8 при у = 2 4/13;

y=2 4/13 =(26+4)/13=30/13

5,2*30/13-12,8=12-12,8=-0,8;

2) 5 1/4 * (12 – с) + 3 1/4 * (–с – 8) = (21/4)*12 -(21/4)c- (13/4)c- (13/4)*8=

=21*3 -(21/4)c- (13/4)c- 13*2 при с = –0,4.

63 -(21/4)*(-0,4)- (13/4)*(-0,4)- 26=37-(-0,4)(-34/4)=37-(34*0,4/4)=37-3,4=33,6

1. на множители
a)
6a²-6b² = 6(a² - b²) = 6(a-b)(a+b)
б)
1+27a³ = (1+3a)(1-3a+9a²)
в)
2a(x+y)+x+y = 2a(x+y)+(x+y) = (x+y)(2a+1) 
г)
3ab³-3a³b = 3ab(b² - a²) = 3ab(b - a)(b + a)
2.Решите выражения
а)
(x-5)(x+5)-(x+10)(x-10) = (x² - 25) - (x² - 100) = x² - 25 - x² + 100 = 75
б)
(5x-2y)²-9y² = (5x-2y)² - (3y)² = (5x - 2y + 3y)(5x - 2y - 3y) =
=(5x + y)(5x - 5y) = 25x² + 5xy - 25xy - 5y² = 25x² - 20xy - 5y² 
в)
(2x-y)(4x²+2xy+y²) =(2x-y)(2x + y)² = (4x² - y²)(2x+y) = 8x³ - 2xy² + 4x² - y³   
3.Решите уравнения
(3x-1)³=27x³-1
27x³ - 27x² + 9x - 1= 27x³ - 1
27x² - 9x = 0
x(27x - 9) = 0
x₁ = 0
27x - 9 = 0
27x = 9
x₂ = 9/27=1/3
ответ: 0; 1/3 

4. Вычислить

77² - 23² = (77 - 23)(77 + 23) = 54 * 100 = 5400