Verified answer

Ответ:

Объяснение:

№1

а) [tex](a-3)^{2} =a^{2} -6a+9[/tex]

б)[tex](2x+y)^{2} =4x^{2} +4xy+y^{2}[/tex]

в)[tex](5b-4x)(5b+4x)=25b^{2} -16x^{2}[/tex]

№2

а) [tex]4a(a-2)-(a-4)^{2} =4a^{2} -8a-(a^{2} -8a+16)=4a^{2} -8a-a^{2} +8a-16=3a^{2} -16[/tex]

б) [tex]2(b+1)^{2} -4b=2(b^{2} +2b+1)-4b=2b^{2} +4b+2-4b=2b^{2} +2=2(b^{2} +1)[/tex]

№3

а) [tex]x^{2} -25=(x+5)(x-5)\\[/tex]

б)[tex]ab^{2} -ac^{2} =a(b^{2} -c^{2})=a(b+c)(b-c)\\[/tex]

в) [tex]-3a^{2} -6ab-3b^{2} =-3(a^{2} +2ab+b^{2})=-3(a+b)^{2}[/tex]

№4

a)[tex]25a^{2} -(a+3)^{2} =(5a+(a+3)(5a-(a+3)=(6a+3)(4a-3)=3(2a+1)(4a-3)[/tex]

б)[tex]27a^{3} +b^{3} =(3a+b)(9a^{2} -3ab+b^{2} )[/tex]

в) [tex]16x^{4} -81=(4x^{2} +9)(4x^{2} -9)=(4x^{2} +9)(2x+3)(2x-3)[/tex]