Đáp án:
Tham khảo
Giải thích các bước giải:
$ A=(x+y)^{2}-(x-y)^{2}$
$=(x+y+x-y)(x+y-x+y)$
=$2x.2y$
$=4xy$
$B=(x-y)^{2}-2(x+y)+(x-y)^{2}$
$=x^{2}+2xy+y^{2}-2x^{2}+2y{2}+x^{2}-2xy+y^{2}$
$=(x^{2}-2x^{2}+x^{2})(2xy-2xy)(2y^{2}+y^{2}+y^{2})$
$=4xy$
$C=(x+y)^{3}-(x-y)^{3}-2y^{3}$
$=x^{3}+3x^{2}y+3xy^{2}+y^{3}-x^{3}+3x^{2}y-3xy^{2}-2y^{3}$
$=(x^{3}-x^{3})(3x^{2}y+3x^{2}y)(3xy^{2}-3xy^{2})(y^{3}+y^{3}-2y^{3})$
$=6x^{2}y$
Bài 3
$ A=(x+y)^{2}-(x-y)^{2}$
$=(x+y+x-y)(x+y-x+y)$
=$2x.2y$
$B=(a+b)^{3}+(a+b)^{3}-2a^{3}$
$=[(a+b)^{2}-2(a+b)(a-b)+(a-b)^{2}]-2a^{3}$
$=2a(a^{2}+2ab+b^{2}-2(a^{2}-b^{2})+a^{2}+b^{2})-2a^{3}$
$=2a(2a^{2}+2b^{2}-2a^{2}-2b^{2})-2a^{3}$
$=2a^{3}$
$C=9^{8}.2^{8}-(18^{4}-1)(18^{4}+1)$
$=9^{8}.2^{8}-(18^{8}-1)$
$=9^{8}.2^{8}-18^{8}-1$
$=9.^{8}.2^{8}-(9.2)^{8}-1$
$=9^{8}.2^{8}-9^{8}.2^{8}-1$
$=-1$
