Упр.412 ГДЗ Муравин 7 класс (Алгебра)

1) а^2 + 2аb + b^2 — с^2; 5) b^2 — с^2 — 14с — 49;
2) x^2 — 2ху + у^2 — z^2; 6) а^2 — х^2 + 10х — 25;
3) а^2 — 18а + 81 — 4b^2; 7) а^2 х^2 — 2abx + b^2 — с^2;
4) у^2 + 20у + 100 — 9x^2; 8) р^2 + k^2 у^2 + 2kpy — х^2.

1. $$a^2+2ab+b^2-c^2=(a+b)^2-c^2=(a+b-c)(a+b+c)$$
2. $$x^2-2xy+y^2-z^2=(x-y)^2-z^2=(x-y-z)(x-y+z)$$
3. $$a^2-18a+81-4b^2=(a-9)^2-(2b)^2=(a-9-2b)(a-9+2b)$$
4. $$y^2+20y+100-9x^2=(y+10)^2-(3x)^2=(y+10-3x)(y+10+3x)$$
5. $$b^2-c^2-14c-49=b^2-(c^2+14c+49)=b^2-(c+7)^2$$
   $$=(b-c-7)(b+c+7)$$
6. $$a^2-x^2+10x-25=a^2-(x^2-10x+25)=a^2-(x-5)^2$$
   $$=(a-x+5)(a+x-5)$$
7. $$a^2x^2-2abx+b^2-c^2=(ax-b)^2-c^2=(ax-b-c)(ax-b+c)$$
8. $$p^2+k^2y^2+2kpy-x^2=(p+ky)^2-x^2=(p+ky-x)(p+ky+x)$$

Ответ

1) $$(a+b-c)(a+b+c)$$
2) $$(x-y-z)(x-y+z)$$
3) $$(a-9-2b)(a-9+2b)$$
4) $$(y+10-3x)(y+10+3x)$$
5) $$(b-c-7)(b+c+7)$$
6) $$(a-x+5)(a+x-5)$$
7) $$(ax-b-c)(ax-b+c)$$
8) $$(p+ky-x)(p+ky+x)$$