Задание 3 Параграф 19 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 7 класс (Алгебра)

1) a^2-6a+9-b^2;
2) 36-a^2+2ac-c^2;
3) (x^2+16)^2-64x^2;
4) 121-81x^2-90xy^2-25y^4.

1. $$a^2-6a+9-b^2=(a-3)^2-b^2$$
   $$=(a-3-b)(a-3+b)$$
2. $$36-a^2+2ac-c^2=36-(a^2-2ac+c^2)$$
   $$=6^2-(a-c)^2$$
   $$=(6-a+c)(6+a-c)$$
3. $$\left(x^2+16\right)^2-64x^2=\left(x^2+16\right)^2-(8x)^2$$
   $$=\left(x^2+16-8x\right)\left(x^2+16+8x\right)$$
   $$=(x^2-8x+16)(x^2+8x+16)$$
   $$=(x-4)^2(x+4)^2$$
   $$=\left((x-4)(x+4)\right)^2$$
   $$=(x^2-16)^2$$
4. $$121-81x^2-90xy^2-25y^4=121-\left(81x^2+90xy^2+25y^4\right)$$
   $$=11^2-\left(9x+5y^2\right)^2$$
   $$=\left(11-9x-5y^2\right)\left(11+9x+5y^2\right)$$

Ответ

1) $$\left(a-3-b\right)\left(a-3+b\right)$$;
2) $$\left(6-a+c\right)\left(6+a-c\right)$$;
3) $$\left(x^2-16\right)^2$$;
4) $$\left(11-9x-5y^2\right)\left(11+9x+5y^2\right)$$.