В решении.
Объяснение:
а)а(а-b)+b(a+b)+(a-b)(a+b)=
=a²-ab+ab+b²+a²-b²=
=2a²;
б)(m-n)(n+m)-(m-n)²+2n²=
=m²-n²-(m²-2mn+n²)+2n²=
=m²-n²-m²+2mn-n²+2n²=
=2mn;
в)(c-d)²-(c+d)(d-c)+2cd=
=c²-2cd+d²-d²+c²+2cd=
=2c²;
г)(2a+5b)(5a-2b)-3(a+2b)(a-2b)=
=(10a²-4ab+25ab-10b²)-3(a²-4b²)=
=10a²+21ab-10b²-3a²+12b²=
=7a²+21ab+2b²;
д)(p+6)²-4(3-p)(3+p)=
=(p²+12p+36)-4(9-p²)=
=p²+12p+36-36+4p²=
=5p²+12p=
=p(5p+12);
е) -(2+m)²+2(1+m)²-2(1-m)(m+1)=
= -(4+4m+m²)+2(1+2m+m²)-2(1-m²)=
= -4-4m-m²+2+4m+2m²-2+2m²=
=3m²-4;
ж)(x+y)²-(x-y)²= разность квадратов
=(х+у-х+у)(х+у+х-у)=
=2у*2х=
=4ху;
з)(m-n)²-(m+n)²= разность квадратов
=(m-n-m-n)(m-n+m+n)=
=(-2n)*2m=
= -4mn.
В решении.
Объяснение:
а)а(а-b)+b(a+b)+(a-b)(a+b)=
=a²-ab+ab+b²+a²-b²=
=2a²;
б)(m-n)(n+m)-(m-n)²+2n²=
=m²-n²-(m²-2mn+n²)+2n²=
=m²-n²-m²+2mn-n²+2n²=
=2mn;
в)(c-d)²-(c+d)(d-c)+2cd=
=c²-2cd+d²-d²+c²+2cd=
=2c²;
г)(2a+5b)(5a-2b)-3(a+2b)(a-2b)=
=(10a²-4ab+25ab-10b²)-3(a²-4b²)=
=10a²+21ab-10b²-3a²+12b²=
=7a²+21ab+2b²;
д)(p+6)²-4(3-p)(3+p)=
=(p²+12p+36)-4(9-p²)=
=p²+12p+36-36+4p²=
=5p²+12p=
=p(5p+12);
е) -(2+m)²+2(1+m)²-2(1-m)(m+1)=
= -(4+4m+m²)+2(1+2m+m²)-2(1-m²)=
= -4-4m-m²+2+4m+2m²-2+2m²=
=3m²-4;
ж)(x+y)²-(x-y)²= разность квадратов
=(х+у-х+у)(х+у+х-у)=
=2у*2х=
=4ху;
з)(m-n)²-(m+n)²= разность квадратов
=(m-n-m-n)(m-n+m+n)=
=(-2n)*2m=
= -4mn.