a) \(\left(x+y\right)^2-\left(x-y\right)^2=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y\cdot2x=4xy\)
b) \(\left(a+b\right)^3+\left(a-b\right)^3-2a^3\)
\(=a^3+3a^2b+3ab^2+b^3+a^2-3a^2b+3ab^2-b^3-2a^3\)
\(=6ab^2\)
c) \(9^8\cdot2^8-\left(18^4-1\right)\left(18^4+1\right)\)
\(=18^8-\left(18^8-1\right)=1\)
a) \(\left(x+y\right)^2-\left(x-y\right)^2=x^2+2xy+y^2-\left(x^2-2xy+y^2\right)\)
\(=x^2+2xy+y^2-x^2+2xy-y^2\)
\(=\left(x^2-x^2\right)+\left(y^2-y^2\right)+\left(2xy+2xy\right)\)
\(=4xy\)
a) (x+y)2-(x-y)2
=(x+y+x-y)(x+y-x+y)
=2x.2y=4xy
b) (a+b)3+(a-b)3-2a3
=(a+b+a-b)(a2+2ab+b2-a2+b2+a2-2ab+b2)-2a3
=2a.(a2+3b2)-2a3
=2a3+6ab2-2a3
=6ab2
a, \(\left(x-y\right)^2-\left(x+y\right)^2\)
\(=\left[\left(x-y\right)-\left(x+y\right)\right].\left[\left(x-y\right)+\left(x-y\right)\right]\)
\(=\left(x-y-x-y\right).\left(x-y+x+y\right)\)
\(=-2y\left(2x\right)\)
\(=-4xy\)
b, \(\left(a+b\right)^3+\left(a-b\right)^3-2a^3\)
\(=\left(a+b\right)^3-a^3+\left(a-b\right)^3-a^3\)
\(=\left(a+b-a\right)\left(a^2+b^2+2ab+a^2+ab+a^2\right)+\left(a-b-a\right)\left(a^2+b^2-2ab-a^2+ab+a^2\right)\)\(=b.\left(3a^2+b^2+3ab\right)-b\left(a^2+b^2-ab\right)\)
\(=b\left(3a^2+b^2+3ab-a^2-b^2+ab\right)\)
\(=b\left(2a^2+4ab\right)\)
c, \(9^8.2^8-\left(18^4-1\right).\left(18^4+1\right)\)
\(=9^8.2^8-\left(18^8-1\right)\)
\(=9^8.2^8-18^8+1\)
\(=1\)
Chúc bạn học tốt nha :)