\(n\left(2n-3\right)-2n\left(n+1\right)\)

\(=2n^2-3n-2n^2-2n\)

\(=5.\left(-n\right)\)chia hết cho 5.

Gọi 4 số nguyên liên tiếp là a ; a + 1 ; a + 2 ; a + 3 \(\left(a\in Z\right)\)

Ta có:

\(a\left(a+3\right)=a^2+3a\)

\(\left(a+1\right)\left(a+2\right)=a^2+3a+2\)

\(\Rightarrow\left(a+1\right)\left(a+2\right)-a\left(a+3\right)\)

\(=a^2+3a+2-\left(a^2+3a\right)\)

\(=2\)

Vậy hơn 2 đơn vị.

  A = (5\(x\) + 1)² + (5\(x\) - 1)² - 2.( 5\(x\) +1).(5\(x\) - 1) tại \(x\) = 1

Thay \(x\) = 1 vào A ta có:

A = (5.1 + 1)² + (5.1 - 1)² - 2.(5.1 + 1).(5.1 - 1)

A = 6² + 4² - 2.6.4 

A = 36 + 16 - 48

A = 52 - 48

A = 4

a) ( -5x² +3xy + 7) + ( -6x²y + 4xy² - 5)=4*x*y^2-6*x^2*y+3*a*x*y-5*a*x^2+7*a-5

b) ( 2,4x³ - 10x²y) + (7x²y - 2,4x³ + 3xy²)=3*x*y^2-3*x^2*y

c) ( 15x²y - 7xy² - 6y²) + (2x² - 12x²y + 7xy²)=-6*y^2+3*x^2*y+2*x^2

d) ( 4x² + x²y - 5y³) + (5/3 x³ - 6xy² - x²y) + (x³/3 + 10y³) + ( 6y³-15xy² - 4x²y - 10x³)=11*y^3-21*x*y^2-4*x^2*y-8*x^3+4*x^2

\(\frac{2x+6}{\left(x+3\right)\left(x-2\right)}=0\left(ĐKXĐ:x\ne-3;x\ne2\right)\)

\(\Rightarrow2x+6=0\Leftrightarrow x=-3\) (loại)

Vậy phương trình vô nghiệm.

ĐKXĐ \(x\ne-3,x\ne2\)

ta có \(\frac{2x+6}{\left(x+3\right)\left(x-2\right)}=0\)

\(\Leftrightarrow\frac{2\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}=0\)

\(\Rightarrow\frac{2}{x-2}=0\)

\(x=2\)(không thỏa mãn Đkxđ)

vậy phương trình vô nghiệm

\(x^2-y^2+z^2-t^2-2xz+2yt\)

\(=\left(x^2+z^2-2xz\right)-\left(y^2+t^2-2yt\right)\)

\(=\left(x-z\right)^2-\left(y-t\right)^2\)

\(=\left(x-z-y+t\right)\left(x-z+y-t\right)\)

x²-y²+z²-t²-2xz+2yt

=(x²-2xz+z²)+(-y²+2yt-t²)

=(x²-2xz+z²)-(y²-2yt+t²)

=(x-z)²-(y-t)²

=(x-z-y+t)(x-z+y-t)

Bạn sửa lại đề bài câu 2) nhé ^^

2) \(a+b+c+d=0\Leftrightarrow a+b=-c-d\Leftrightarrow\left(a+b\right)^3=-\left(c+d\right)^3\)

\(\Leftrightarrow a^3+b^3+3ab\left(a+b\right)=-\left[c^3+d^3+3cd\left(c+d\right)\right]\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=-3cd\left(c+d\right)-3ab\left(a+b\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=3ab\left(c+d\right)-3cd\left(c+d\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=3\left(c+d\right)\left(ab-cd\right)\)

đề đúng ak bạn

99.100 = 9900

(20.1)² = 20² = 400

73² - 27² = (73 - 27).(73 + 27) = 46.100 = 4600

Ủng hộ mk nha ^_-

99,100=9900

(20,1) \(^2\)=20\(^2\) =400

73\(^2\) -27\(^2\) =(73-27),(73+27)=46,100=4600

ủng hộ giùm nha ^^

c) \(-\frac{x^4}{4}+2x^2y^3-4y^6=-\left(\frac{x^4}{4}-2x^2y^3+4y^6\right)=-\left[\left(\frac{x^2}{2}\right)^2-2.\frac{x^2}{2}.2y^3+\left(2y^3\right)^2\right]=-\left(\frac{x^2}{2}-2y^3\right)\)