Упр.297 ГДЗ Никольский Потапов 7 класс (Алгебра)

б) -(x-y)(x+y)
в) -(х — у)(х — у);
г) -(2m-n)(n-3m);
д) -(5а — 2b)(3b + 2а);
е) -7(x+8y)(y-3x).

1. $$-(a+b)(a+b)=-(a+b)^2=-a^2-2ab-b^2.$$

2. $$-(x-y)(x+y)=-(x^2-y^2)=-x^2+y^2.$$

3. $$-(x-y)(x-y)=-(x-y)^2=-x^2+2xy-y^2.$$

4. $$-(2m-n)(n-3m)=-(2mn-6m^2-n^2+3mn)$$

   $$= -(-6m^2+5mn-n^2)=6m^2-5mn+n^2.$$

5. $$-(5a-2b)(3b+2a)=-(15ab+10a^2-6b^2-4ab)$$

   $$=-(10a^2+11ab-6b^2)=6b^2-11ab-10a^2.$$

6. $$-7(x+8y)(y-3x)=-7(xy-3x^2+8y^2-24xy)$$

   $$=-7(-3x^2-23xy+8y^2)=21x^2+161xy-56y^2.$$

Ответ

а) $$-a^2-2ab-b^2$$; б) $$-x^2+y^2$$; в) $$-x^2+2xy-y^2$$; г) $$6m^2-5mn+n^2$$; д) $$6b^2-11ab-10a^2$$; е) $$21x^2+161xy-56y^2$$.