Bài 1:
a, ( x+2y)^2= x^2+4xy+4y^2
b, (3x-2y)^2= 9x^2 -12xy+4y^2
c, ( x-2)(x^2+2x+4)=(x-2)^
d, (a + b + c)^2
= [(a + b) + c]^2
= (a + b)^2 + 2(a + b)c + c^2
= a^2 + 2ab + b^2 + 2ac + 2bc + c2
= a2 + b2 + c2 + 2ab + 2bc + 2ac
e) (a + b – c)2
= [(a + b) – c]2
= (a + b)2 – 2(a + b)c + c2
= a2 + 2ab + b2 – 2ac – 2bc + c2
= a2 + b2 + c2 + 2ab – 2bc – 2ac
f, (a – b – c)2
= [(a – b) – c]2
= (a – b)2 – 2(a – b)c + c2
= a2 – 2ab + b2 – 2ac + 2bc + c2
= a2 + b2 + c2 – 2ab + 2bc – 2ac.
Bài 2:
a. x^3 + 8y^3
= x^3 + (2y)^3
= (x+2y) ( x^2 - 2xy + 4y^2)
b. a^6-b^3
=(a^2)^3-b^3
=(a^2-b)[(a^2)^2+2ab+b^2]
=(a^2-b)(a^4+2ab+b^2)
c. 8y^3-125
= 2^3 . y^3 - 5^3
= (2.y)^3 - 5^3
= (2y - 5) [(2y)^2 + 2y.5 + 5^2]
= (2y - 5) [(2y)^2 + 2y.5 +25]
d. 8z^3+27
=(2z)^3−3^3
=(2z−3)[(2z)^2+6z+3^2]
=(2z−3)(4z^2+6z+9)
Bài 3 :
a,(a+b+c)^2+(a+b-c)^2+(2a+b)^2
=a^2+b^2+c^2+ 2ab+2bc+2ac+(a+b-c)(a+b-c)-(4a^2+4ab+b^2)
=a^2+b^2+c^2+ 2ab+2bc+2ac+a^2+ab-ac+ab+b^2-bc-ac-bc+c^2-2a^2-4ab-2b^2
=2c^2
b, 100^2-99^2+98^2-97^2+.....+2^2-1^2
=(100-99)(100+99)+(98-97)(98+97)+.....+(2-1)(2+1)
=100+99+98+97+....+2+1
=(1+100).100:2
=5050
c, 3(2^2+1)(2^4+1)(2^8+1).....(2^64+1)+1
=3(2^2+1)(2^2-1)(2^4+1)(2^4-1)....(2^64+1)+1
=3(2^4+1)(2^4-1)....(2^64+1)+1
=3(2^64-1)(2^64+1)+1
=3.(2^128+1-1)
=3.2^128
Chúc bạn học tốt ^_^
