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1) \(x^6+1\)
\(=x^6+x^4-x^4+x^2-x^2+1\)
\(=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)
\(=x^2\left(x^4-x^2+1\right)+\left(x^4-x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
2) \(x^6-y^6\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
Ta có: \(x^2\cdot\left(x^4+25\right)\cdot\left(x^2-5\right)\cdot\left(x^2+5\right)\cdot\left(x-y\right)\left(x^2+xy+y^2\right)\cdot\left(x^3+y^3\right)\)
\(=x^2\cdot\left(x^4+25\right)\left(x^4-25\right)\cdot\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=x^2\cdot\left(x^8-625\right)\cdot\left(x^6-y^6\right)\)
a) \(-\left(x+2\right)\cdot\left(x^2-1x+4\right)\)
\(=-\left(x+2\right)\cdot\left(x^2-x+4\right)\)
\(=-\left(x^3-x^2+4x+2x^2-2x+8\right)\)
\(=-\left(x^3+x^2+2x+8\right)\)
\(=-x^3-x^2-2x-8\)
b) \(-\left(x+2y\right)\cdot\left(x^2-2xy+y^2\right)\)
\(=-\left(x^3-2x^2y+xy^2+2x^2y-4xy^2+2y^3\right)\)
\(=-\left(x^3-3xy^2+2y^3\right)\)
\(=-x^3+3xy^2-2y^3\)
c) \(-\left(5-a\right)\cdot\left(25+5a+a^2\right)\)
\(=-\left(125-a^3\right)\)
\(=-125+a^3\)
d) \(-\left(x-2y\right)\cdot\left(x^2+2xy+4y^2\right)\)
\(=-\left(x^3-8y^3\right)\)
\(=-x^3+8y^3\)
a)\(-25+4x^2=\left(2x-5\right)\left(2x+5\right)\)
b)\(-x^2+10x-25=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)
c)\(\frac{1}{9}x^2+\frac{2}{3}xy+y^2=\left(\frac{1}{3}x+y\right)^2\)
\(a,-25+4x^2=4x^2-25=\left(2x-5\right)\left(2x+5\right)\)
\(b,-x^2+10x-25=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)
\(c,\frac{1}{9}x^2+\frac{2}{3}xy+y^2=\left(\frac{1}{3}x\right)^2+\frac{2.1}{3}xy+y^2=\left(\frac{1}{3}x+y\right)^2\)(sửa đề)
A = 262 - 242 = (26 - 24)(26 + 24) = 2.50 = 100
B = 272 - 252 = (27 - 25)(27 + 25) = 2.52 = 104
\(A=26^2-24^2\)
\(A=\left(26-24\right)\left(26+24\right)\)
\(A=2.50\)
\(B=27^2-25^2\)
\(B=\left(27-25\right)\left(27+25\right)\)
\(B=2.52\)
\(2.50< 2.52\)
\(< =>A< B\)
252 - 152
= (25 - 15)(25 + 15)
= 10 . 40
= 400
2052 - 952
= (205 - 95)(205 + 95)
= 110 . 300
= 33 000
362 - 142
= (36 - 14)(36 + 14)
= 22 . 50
= 1 100
9502 - 8502
= (950 - 850)(950 + 850)
= 100 . 1 800
= 180 000
cảm ơn nhé