Упростите выражение: 1) (5а+4)^2-40а 2) 16х^2-4(2х+3)^2 3) (3b-2)^2+12b 4) -25x^2+(5х-4)^2 5) (3а-7b)^2+42ab 6) (a+(b-c))^2 7) (2a+6b)^2-24ab 8) (a-(b+c))^2

1) [latex] (5a+4)^{2}-40a= 25a^{2}+40a+16-40a= 25a^{2}+16 [/latex] 2) [latex]16x^{2}-4*(2x+3)^{2}= 16x^{2}-16x^{2}-48x-36=-48x-36=[/latex][latex]-12(4x+3) [/latex] 3) [latex] (3b-2)^{2} +12b=9 b^{2} -12b+4+12b=9 b^{2} +4[/latex] 4) [latex]-25 x^{2}+(5x-4)^{2}=-25x^{2}+25 x^{2} -40x+16=16-40x=8(2-5x)[/latex] 5) [latex] (3a-7b)^{2}+42ab=9 a^{2} -42ab+49 b^{2}+42ab=9 a^{2} +49 b^{2} [/latex] 6) [latex] (a+(b-c))^{2}= (a+b-c)^{2}=(a+b-c)*(a+b-c)=[/latex][latex]a^{2}+ab-ac+ab+ b^{2}-bc-ac-bc+c^{2}=[/latex][latex]a^{2}+b^{2}+c^{2}+2ab-2ac-2bc[/latex] 7) [latex] (2a+6b)^{2}-24ab=4 a^{2} +24ab+36 b^{2}-24ab=4a^{2} +36 b^{2}=[/latex][latex]4(a^{2} +9 b^{2}) [/latex] 8) [latex] (a-(b+c))^{2} = (a-b-c)^{2} =(a-b-c)*(a-b-c)=[/latex][latex](a-b-c)*(a-b-c)= a^{2}-ab-ac-ab+ b^{2} +bc-ac+bc+ c^{2} = [/latex][latex] a^{2}-ab-ac-ab+ b^{2} +bc-ac+bc+ c^{2} =[/latex][latex]a^{2}+b^{2}+c^{2}-2ab-2ac+2bc[/latex]