Упр.145 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) x^2+2xy+y^2-64;
2) m^2+16n^2+8mn-b^2;
3) x^2 y^3-xy+y-y^3;
4) a^3+27-3a-a^2;
5) x^12-6x^10+9x^8-36;
6) b^3+64a^3+b^2+8ba+16a^2;
7) x^2-6xy+9y^2-a^2-2a-1;
8) 4x^2-y^2-4x+1.

1. $$x^2+2xy+y^2-64=(x+y)^2-8^2=(x+y-8)(x+y+8).$$
2. $$m^2+16n^2+8mn-b^2=(m^2+8mn+16n^2)-b^2=(m+4n)^2-b^2$$
   $$=(m+4n-b)(m+4n+b).$$
3. $$x^2y^3-xy+y-y^3=(x^2y^3-y^3)-(xy-y)=y^3(x^2-1)-y(x-1)$$
   $$=y^3(x-1)(x+1)-y(x-1)=(x-1)\bigl(y^3(x+1)-y\bigr)$$
   $$=y(x-1)(xy^2+y^2-1).$$
4. $$a^3+27-3a-a^2=(a^3+27)-a(a+3)$$
   $$=(a+3)(a^2-3a+9)-a(a+3)$$
   $$=(a+3)(a^2-4a+9).$$
5. $$x^{12}-6x^{10}+9x^8-36=x^8(x^4-6x^2+9)-36$$
   $$=x^8(x^2-3)^2-6^2=(x^4(x^2-3)-6)(x^4(x^2-3)+6)$$
   $$=(x^6-3x^4-6)(x^6-3x^4+6).$$
6. $$b^3+64a^3+b^2+8ba+16a^2=(b^3+64a^3)+(b^2+8ab+16a^2)$$
   $$=(b+4a)(b^2-4ab+16a^2)+(b+4a)^2$$
   $$=(b+4a)(b^2-4ab+b+16a^2+4a)$$
   $$=(b+4a)(b^2-4ab+b+4a+16a^2).$$
7. $$x^2-6xy+9y^2-a^2-2a-1=(x-3y)^2-(a+1)^2$$
   $$=(x-3y-a-1)(x-3y+a+1).$$
8. $$4x^2-y^2-4x+1=(4x^2-4x+1)-y^2=(2x-1)^2-y^2$$
   $$=(2x-1-y)(2x-1+y).$$

Ответ

1) $$(x+y-8)(x+y+8)$$
2) $$(m+4n-b)(m+4n+b)$$
3) $$y(x-1)(xy^2+y^2-1)$$
4) $$(a+3)(a^2-4a+9)$$
5) $$(x^6-3x^4-6)(x^6-3x^4+6)$$
6) $$(b+4a)(b^2-4ab+b+4a+16a^2)$$
7) $$(x-3y-a-1)(x-3y+a+1)$$
8) $$(2x-1-y)(2x-1+y)$$