75 x ( 4²⁰¹⁵ + 4²⁰¹⁴ +  4²⁰¹³ + .... 4 + 1 ) +25 

= 25 x  3 x (4 ²⁰¹⁵ + 4²⁰¹⁴ + ... 1 ) + 25

= 25 x 3 + 25 x ( 4²⁰¹⁵+ .... + 1)

 = 100 x ( 4²⁰¹⁵+4²⁰¹⁴ + ..... + 1 )

=> chia hết cho 100

Mìn đang nghĩ bài 1 , nếu làm được mìn sẽ giúp 

khó

Chỗ 25 x 3 + 25 nhớ đóng ngoặc nha

\(a,VP=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\\ =\left(x+2y\right)\left[x^2-x.2y+\left(2y\right)^2\right]\\ =x^3+\left(2y\right)^3=x^3+8y^3=VT\left(đpcm\right)\\ b,VT=\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\left(x-y\right)\\ =x^3-y^3-3xy\left(x-y\right)\\ =x^3-3x^2y+3xy^2-y^3\\ =\left(x-y\right)^3=VP\left(đpcm\right)\)

\(c,VT=\left(x-3y\right)\left(x^2+3xy+9y^2\right)-\left(3y+x\right)\left(9y^2-3xy+x^2\right)\\ =\left(x-3y\right)\left[x^2+x.3y+\left(3y\right)^2\right]-\left(x+3y\right).\left[x^2-x.3y+\left(3y\right)^2\right]\\ =x^3-27y^3-\left(x^3+27y^3\right)\\ =-54y^3=VP\left(đpcm\right)\)

x(3y + 5 ) = - 2 - 4y  => \(x=-\frac{4y+2}{3y+5}=-1-\frac{y-3}{3y+5}\in Z\)=> y -3 =0  hoặc y-3 = 3y+5 hoặc y -3 = -( 3y+5) hoặc 3y +5 = 1 hoặc 3y+5 =-1

=> y thuộc {3; -4 ; -2 } => x  tương ứng { -1; -2 ; -6}

Vậy (x;y) = (-1;3) ; ( -2; -4) ; ( -6; -2) 

Ta có: 5x^2 + 3xy = 8

=> 5.x.x + 3xy = 8

=> x^2.(5+3).y=8

=> x^2.8.y=8

=> x^2.y=1

=> x^2.y = 1.1= -1.-1= -1.1 = 1.-1

=>3xy-3x=6

=>3x(y-1)=6

=>x(y-1)=2

=>\(\left(x;y-1\right)\in\left\{\left(1;2\right);\left(2;1\right);\left(-1;-2\right);\left(-2;-1\right)\right\}\)

=>\(\left(x,y\right)\in\left\{\left(1;3\right);\left(2;2\right);\left(-1;-1\right);\left(-2;0\right)\right\}\)