Question

Разложите на множители: а) (х+у)^2-(х-у)^2 б) (2m-n)^2-(m+2n)^2 в) (3n+2p)^2-(5p-2n)^2 г) 4(3х-2у)^2-9(4х+3у)^2 д) 100(6а+3b^2-81(3a+2b)^2 e) 49(5x^2+8)^2-36(4x^2-1)^2

Answer 1

$1)(x+y)^{2}-(x-y)^{2}=x^{2}+2xy+y^{2}-x^{2}+2xy-y^{2}=4xy$
$2)(2m-n)^{2}-(m+2n)^{2}=4m^{2}-4mn+n^{2}-m^{2}-4mn-4n^{2}=$$3m^{2}-8mn-3n^{2}$
$3)(3n+2p)^{2}-(5p-2n)^{2}=6n^{2}+12pn+4p^{2}-25p^{2}+20pn-4n^{2}=$$2n^{2}+32pn-21p^{2}$
$4(3x-2y)^{2}-9(4x+3y)^{2}=4(9x^{2}-12xy+4y^{2})-9(16x^{2}+24xy+$$9y^{2})=36x^{2}-48xy+16y^{2}-144x^{2}-216xy-81y^{2}=-108x^{2}-264xy$$-65y^{2}$
$5)100(6a+3b)^{2}-81(3a+2b)^{2}=100(36a^{2}+36ab+9b^{2})-81(9a^{2}+$$12ab+4b^{2})=3600a^{2}+3600ab+900b^{2}-729a^{2}-972ab-324b^{2}=$$2871a^{2}+2628ab+576b^{2}$
$6)49(5x^{2}+8)^{2}-36(4x^{2}-1)^{2}=49(25x^{4}+80x^{2}+64)-36(16x^{4}-$$8x^{2}+1)=1225x^{4}+3920x^{2}+3136-576x^{4}+288x^{2}-36=$$649^{4}+4208x^{2}+3100$