a2 ( 1 + a ) - b2 ( 1 - b ) - a2b2 ( a + b)
= a2 + a3 - b2 + b3 - a2b2 ( a + b)
= ( a2 - b2) + ( a3 + b3) - a2b2 ( a + b)
= ( a - b )( a + b) - ( a + b)( a2- ab + b2 ) - a2b2 ( a + b)
= ( a + b )( a - b - a2 + ab - b2 - a - b)
a2 ( 1 + a ) - b2(1-b)-a2b2(a+b)
= a2 + a3 -b2 + b3 -a2b2(a+b)
=( a2 - b2) + (a3+b3)-a2b2(a+b)
=( a-b)(a+b) + (a+b)(a2 -ab + b2) - a2b2(a+b)
= (a+b)(a-b+a2 -ab + b2- a2b2)
Rút gọn các biểu thức:
\(A=\left(5a+5\right)^2+10\left(a-3\right)\left(1+a\right)+a^2-6a+9\)
B = \(\left(6a-2\right)^2+4\left(3a-1\right)\left(1-2b\right)\left(2b-1\right)^2\)
Bài 1 :
a) \(\left(6x^2+\frac{1}{3}\right)^2\)
b) \(\left(5x-4y\right)^2\)
c) \(\left(2x^2y-3y^2x\right)^2\)
d) \(\left(5x-3\right).\left(5x+3\right)\)
e) \(\left(-4xy-5\right).\left(5-4xy\right)\)
f) \(\left(a^2b+ab^2\right).\left(ab^2-a^2b\right)\)
g) \(\left(3x-4\right)^2+2.\left(3x-4\right).\left(4-x\right)+\left(4-x\right)^2\)
h) \(\left(a^2+ab+b^2\right).\left(a^2-ab+b^2\right)-\left(a^4+b^4\right)\)
Cho \(\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2\) =\(\left(a+b-2c\right)^2+\left(b+c-2a\right)^2+\left(c+a-2b\right)^2\) .CMR:a=b=c
Rút gọn
a) \(A=\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(5x+5\right)^2\)
b) \(B=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{18}+1\right)\left(3^{32}+1\right)\)
c) \(C=\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)
d) \(D=\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-b-a\right)^2\)
e)\(E=\left(a+b+c+d\right)^2+\left(a+b-c-d\right)^2+\left(a+c-b-d\right)^2+\left(a+d-b-c\right)^2\)
1,Cho \(a^2+b^2+c^2+3=2\left(a+b+c\right)\) .Cmr: \(a=b=c=1\)
2,Cho \(\left(a+b+c\right)^2=3\left(ab+ac+bc\right)\) .Cmr: \(a=b=c\)
3,Cho \(\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=\left(a+b-2c\right)^2+\left(b+c-2a\right)^2+\left(c+a-2b\right)^2\) .Cmr: \(a=b=c\)
4,Cho a,b,c,d là các số khác 0 và:
\(\left(a+b+c+d\right)\left(a-b-c+d\right)=\left(a-b+c-d\right)\left(a+b-c-d\right)\) .Cmr: \(\dfrac{a}{c}=\dfrac{b}{d}\)
5,Cho \(x^2-y^2-z^2=0\) .Cmr: \(\left(5x-3y+4z\right)\left(5x-3y-4z\right)=\left(3x-5y\right)^2\)
HELP ME!mik cần gấp lắm rồi!Thank trước nhé!
Bài 1: Tìm x
a) \(\left(5-2x\right)^2-16=0\)
b) \(x^2-4x=29\)
c) \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+9.\left(x+1\right)^2=15\)
d) \(2.\left(x-5\right).\left(x+5\right)-\left(x+2\right).\left(2x-3\right)+x.\left(x^2-8\right)=\left(x+1\right).\left(x^2-x+1\right)\)
Bài 2: Rút gọn
a) \(\left(x^2+x+1\right).\left(x^2-x+1\right).\left(x^2-1\right)\)
b) \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2.\left(b-c\right)^2\)
c) \(\left(a+b+c\right)^2-\left(a+b\right)^2-\left(a+c\right)^2-\left(b+c\right)^2\)
d) \(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)
cho a + b =1.
Tính \(M=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\left(a+b\right)\)
Rút gọn các biểu thức sau :
a) \(\left(x^2-2x+2\right)\left(x^2-2\right)\left(x^2+2x+2\right)\left(x^2+2\right)\)
b) \(\left(x+1\right)^3+\left(x-1\right)^3-x^3-3x\left(x+1\right)\left(x-1\right)\)
c) \(\left(a+b+c\right)^2+\left(a+b-c\right)^2+\left(2a-b\right)^2\)
d) \(100^2-99^2+98^2+97^2+......+2^2-1^2\)
e) \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)+...+\left(2^{64}+1\right)+1\)
f) \(\left(a+b+c\right)^{^{ }2}+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
Cho \(a^2+b^2+c^2=m\)
Tính GTBT theo m:
\(A=\left(2a+2b-c\right)^2+\left(2b+2c-a\right)^2+\left(2c+2a-b\right)^2\)
