a: \(=\left(892+108\right)^2=1000^2=1000000\)

b: \(=\left(36-26\right)^2=10^2=100\)

c: \(=9.8\cdot10+10.2\cdot10=20\cdot10=200\)

Lời giải:

\(892^2+892.216+108^2=892^2+2.892.108+108^2\)

\(=(892+108)^2=1000^2=1000000\)

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\(10,2.9,8-9.8.0,2+10,2^2-10,2.0,2\)

\(=9,8(10,2-0,2)+10,2(10,2-0,2)\)

\(=9,8.10+10,2.10=10(9,8+10,2)=10.20=200\)

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\(36^2+26^2-52.36=36^2-2.36.26+26^2\)

\(=(36-26)^2=10^2=100\)

a) 2004² - 16

= 2004² - 4²

= (2004 - 4)(2004 + 4)

= 2000.2008

= 4016000

b) 892² + 892.216 + 108²

= 892² + 2.892.108 + 108²

= (892 + 108)²

= 1000²

= 1000000

c) 10,2.9,8 - 9,8.0,2 + 10,2.0,2

= 9,8(10,2 - 0,2) + 2,04

= 9,8.10 + 2,04

= 98 + 2,04

= 100,04

d) 36² + 26² - 52.36

= 36² - 2.36.26 + 26²

= (36 - 26)²

= 10²

= 100

\(A=2004^2-16=\left(2004-4\right)\left(2004+4\right)=2000\cdot2008=4016000\)

\(B=892^2+892\cdot216+108^2=892^2+2\cdot892\cdot108+108^2=\left(892+108\right)^2=1000^2=1000000\)

\(C=10,2\cdot9,8-9,8\cdot0,2+10,2^2-10,2\cdot0,2\)

\(=9,8\left(10,2-0,2\right)+10,2\left(10,2-0,2\right)\)

\(=10\cdot\left(9,8+10,2\right)=10\cdot20=200\)

\(D=36^2+26^2-52\cdot36=\left(36-26\right)^2=10^2=100\)

\(E=105^2-25=\left(105-5\right)\left(105+5\right)=100\cdot110=11000\)

\(F=73^2-27^2=\left(73-27\right)\left(73+27\right)=46\cdot100=4600\)

A. 2004²-16=2004²-4²=(2004-4)(2004+4)=2000.2008=2016000
B. 892²+892.216+108²= 892²+2.892.108+108²=(892+108)²=1000²=1000000
C.Khó nhìn quá
D.36²+26²-52.36=36²-2.36.26+26²=(36-16)²=20²=400
E.105²-25=(105-5)(105+5)=100.110=11000
F. 73²-27²=(73-27)(73+27)=46.100=4600

bài 1.

a.\(\left(x+4\right)\left(x^2-4x+16\right)=x^3-4^3=x^3-64\)

b.\(\left(x^2-\frac{1}{3}\right)\left(x^4+\frac{1}{3}x^2+\frac{1}{9}\right)=\left(x^2\right)^3-\left(\frac{1}{3}\right)^3=x^6-\frac{1}{27}\)

bài 2.

a.\(892^2+892.216+108^2=892^2+2.892.108+108^2\)

\(=\left(892+108\right)^2=1000^2=1_{ }000_{ }000\)

b.\(36^2+26^2-52.36=36^2+26^2-2.26.36=\left(36-26\right)^2=10^2=100\)

Bài 4:

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

\(5\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(5-y\right)\)

\(x^2-12x+36=\left(x-6\right)^2\)

Phân tích đa thức thành nhân tử:

\(6xy+5x-5y-3x^2-3y^2\)

\(=-3x^2+6xy-3y^2+5x-5y\)

\(=-3\left(x^2-2xy+y^2\right)+5\left(x-y\right)\)

\(=-3\left(x-y\right)^2+5\left(x-y\right)\)

\(=\left(x-y\right)\left[-3\left(x-y\right)+5\right]\)

\(=\left(x-y\right)\left(-3x+3y+5\right)\)

Thực hiện phép tính:

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

\(=\left[x^2+\left(x-3\right)\right]\left[x^2-\left(x-3\right)\right]\)

\(=\left(x^2\right)^2-\left(x-3\right)^2\)

\(=x^4-\left(x^2-6x+9\right)\)

\(=x^4-x^2+6x-9\)

b)\(\left(5x-1\right)\left(x+3\right)-\left(x-2\right)\left(5x-4\right)\)

\(=\left(5x^2+15x-x-3\right)-\left(5x^2-4x-10x+8\right)\)

\(=5x^2+15x-x-3-5x^2+4x+10x-8\)

\(=28x-11\)

Tính nhanh:

a)\\(2004^2-16\\)

\\(=2004^2-4^2\\)

\\(=\\left(2004-4\\right)\\left(2004+4\\right)\\)

\\(=2000.2008\\)

\\(=40160000\\)

b)\\(892^2+892.216+108^2\\)

\\(=892^2+2.892.108+108^2\\)

\\(=\\left(892+108\\right)^2\\)

\\(=1000^2\\)

\\(=1000000\\)

c)\\(10,2.9,8-9,8.0,2+10,2^2-10,2.0,2\\)

\\(=9,8\\left(10,2-0,2\\right)+10,2\\left(10,2-0,2\\right)\\)

\\(=9,8.10+10,2.10\\)

\\(=10\\left(9,8+10,2\\right)\\)

\\(=10.20\\)

\\(=200\\)