a)\(69^2-31^2=\left(69-31\right)\left(69+31\right)=38.100=3800\)

\(1023^2-23^2=\left(1023-23\right)\left(1023+23\right)=1000.1046=1046000\)

\(c,\left(27+73\right)^2-2.27.73+54.73\)

\(100^2-54.73+54.73=10000\)

\(d,\left(63-13\right)^2+2.13.63-26.63=50^2=2500\)

a) \(25^2-15^2=\left(25-15\right)\left(25+15\right)=10.40=400\)

b) \(87^2+73^2-27^2-12^2\)

\(=\left(87^2-13^2\right)+\left(73^2-27^3\right)\)

\(=\left(87-13\right)\left(87+13\right)+\left(73-27\right)\left(73+27\right)\)

\(=74.100+100.46\)

\(=100\left(74+46\right)\)

\(=100.120=12000\)

a) 25²-152                                                                       b) 87²+73²-27²-13²                                                         

=(25-15)(25+15)                                                                =(87²-13²)+(73²-27²)

=10*30                                                                             =[(87-13)(87+13)]+[(73-27)(73+27)]

=300                                                                                =7400+4600

                                                                                        =12000

Giải:

1). \(25^2-15^2\)

\(=\left(25-15\right)\left(25+15\right)\)

\(=10.40\)

\(=400\)

2). \(87^2+73^2-27^2-13^2\)

\(=\left(87^2-13^2\right)+\left(73^2-27^2\right)\)

\(=\left(87-13\right)\left(87+13\right)+\left(73-27\right)\left(73+27\right)\)

\(=74.100+46.100\)

\(=100\left(74+46\right)\)

\(=100.120\)

\(=12000\)

Chúc bạn học tốt!!!

Bài 1 :

Theo giả thiết đã ra ta có :

\(n^2\left(n+1\right)+2n\left(n+1\right)\)

\(=\left(n+1\right)\left(n^2+2n\right)=n\left(n+1\right)\left(n+2\right)\) .

\(n\left(n+1\right)\left(n+2\right)\) là tích của 3 số nguyên liên tiếp nên luôn chia hết cho 6 .

Vì vậy \(n^2\left(n+1\right)+2n\left(n+1\right)\) luôn chia hết cho 6 với mọi số nguyên n ( đpcm )

Bài 2 :

Câu a : \(25^2-15^2=\left(25-15\right)\left(25+15\right)=10.40=400\)

Câu b : \(87^2+73^2-27^2-13^2=\left(87^2-13^2\right)+\left(73^2-27^2\right)\)

\(=\left(87+13\right)\left(87-13\right)+\left(73+27\right)\left(73-27\right)=100.74+100.46\)

\(=100\left(74+46\right)=100.120=12000\)

Bài 3 :

Câu a :

\(x^3-0,25x=0\)

\(\Leftrightarrow x\left(x^2-0,25\right)=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x^2-0,25\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x=\dfrac{1}{2}\end{matrix}\right.\)

Vậy \(x=0\) và \(x=\dfrac{1}{2}\)

Câu b :

\(x^2-10x=-25\)

\(\Leftrightarrow x^2-10x+25=0\)

\(\Leftrightarrow\left(x-5\right)^2=0\)

\(\Rightarrow x=5\)

Vậy \(x=5\)

Tính nhanh : 

a) 25² - 15² = (25 + 15)(25 - 15) = 40 . 10 = 400

b) 87² + 73² - 27² - 13² = (87² - 13²) + (73² - 27²)

= (87 + 13)(87 - 13) + (73 + 27)(73 - 27)

= 100 . 74 + 100 . 26 = 100 . (74 + 26) = 100 . 100 = 10000

Bài 1:

a)\(\left(x+y\right)^2-\left(x-y\right)^2=\left(x+y+x-y\right)\left(x+y-x+y\right)=2x\cdot2y=2\left(x+y\right)\)

b) \(\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1+x+1\right)\left(3x+1-x-1\right)\\ =\left(4x+2\right)\cdot2x=4x\left(2x+1\right)\)

Bài 2:

a) \(25^2-15^2=\left(25-15\right)\left(25+15\right)=10\cdot40=400\)

b) \(87^2+73^2-27^2-13^2=\left(87^2-27^2\right)+\left(73^2-13^2\right)\\ =\left(87-27\right)\left(87+27\right)+\left(73-13\right)\left(73+13\right)\)

\(=60\cdot114+60\cdot86=60\cdot\left(114+86\right)=60\cdot200=12000\)

Bài 2:

a) \(x^3-0,25\cdot x=0\)

\(\Leftrightarrow x^2\left(x-0,25\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x-0,25=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=0,25\end{array}\right.\)

b) \(x^2-10=-25\)

\(\Leftrightarrow x^2=-15\) (vô nghiệm0

c) \(4x^2-4x=-1\)

\(\Leftrightarrow4x^2-4x+1=0\)

\(\Leftrightarrow\left(2x-1\right)^2=0\)

\(\Leftrightarrow2x-1=0\Leftrightarrow x=\frac{1}{2}\)

d) \(8x^3+12x^2+6x+1=0\)

\(\Leftrightarrow\left(2x+1\right)^3=0\)

\(\Leftrightarrow2x+1=0\Leftrightarrow x=-\frac{1}{2}\)

Phân tích thành nhân tử : 

a) (x + y)² - (x - y)² = [(x + y) + (x - y)][(x + y) - (x - y)]

= 2x . 2y = 4xy

b) (3x + 1)² - (x + 1)² = [(3x + 1) + (x + 1)][(3x + 1) - (x - 1)]

= (4x + 2)(2x + 2) = 4 . (2x + 1)(x + 1)

a, 25^2 - 15^2 = ( 25 - 15 )( 25 + 15) = 10 . 40 = 400

b, 87^2 + 73^2 - 27^2 - 13^2 

 = 87^2 - 27^2 + 73^2 - 13^2

 = ( 87 - 27)( 87 + 27) + (73 - 13 )(73+ 13)

  =  60 . 114 + 60 . 86

  = 60( 114 + 86)

   = 60 .200 

  = 12000

 c,  x^3 + 27  + 9 x^2 + 27x

= x^3 + 27x + 9x^2 + 27

=(x + 3)^3 

thay x =97 ta có

= (97 + 3)^3

= 100^3

=1000000

d, 1,6^2 + 4.0,8.3,4 + 3,4^2 ( nè 3,4^2 chứ không phải 3,42)

  = 1,6^2 + 2.2.0,8.3,4 + 3,4^2

  =1,6^2 + 2.1,6.3,4 + 3,4^2

  = (1,6 + 3,4)^2

  = 5^2

   = 25

e, x = 11 => 12 =x + 1 thay vào ta có

 x^4 - ( x+ 1)x^3 + (x+1)x^2 -(x+1)x + 11

= x^4 - x^4 - x^13 + x^3 + x^2 - x^2 - x + 11

= -x + 11

= -11 + 11

= 0

ĐÚng ch o tui nha  

87²+73²-27²-13²

 =(87²-13²)+(73²-27²)

=(87+13)(87-13)+(73+27)(73-27)

=100.74+100.46

=100.(74+46)

=100.120

=12000

=12000

đúng cho mk nha

mk pải off rùi

\(\left(x+y\right)^2-\left(x-y\right)^2\)

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

\(=2y.2x\)

\(=4xy\)

b)  (3x+1)²-(x+1)²

=(3x+1+x+1)[(3x+1)-(x+1)]

=(4x+2)2x

=2(2x+1)2x

=4x(2x+1)

c) x³+y³+z³-3xyz

=(x+y)³-3xy(x+y)+z³-3xyz

=[(x+y)³+z³]-3xy(x+y+z)

=(x+y+z)[(x+y)²-z(x+y)+z²]-3xy(x+y+z)

=(x+y+z)(x²+2xy+y²-xz-zy+z²-3xy)

=(x+y+z)(x²+y²+z²-xy-yz-zx)