Упр.132 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) a^2-14a+49; 5) x^10-6x^5 b+9b^2;
2) 25y^2+10y+1; 6) 36m^6+n^12+12m^3 n^6;
3) 100a^2-180ab+81b^2; 7) 1/196 x^8-2x^4 y^2+196y^4;
4) 16m^2+49n^2-56mn; 8) 81/16 a^6-9a^3 b^2+4b^4.

1. $$a^2-14a+49=a^2-2\cdot 7a+7^2=(a-7)^2$$
2. $$25y^2+10y+1=(5y)^2+2\cdot 5y\cdot 1+1^2=(5y+1)^2$$
3. $$100a^2-180ab+81b^2=(10a)^2-2\cdot 10a\cdot 9b+(9b)^2=(10a-9b)^2$$
4. $$16m^2+49n^2-56mn=16m^2-56mn+49n^2=(4m)^2-2\cdot 4m\cdot 7n+(7n)^2=(4m-7n)^2$$
5. $$x^{10}-6x^5b+9b^2=(x^5)^2-2\cdot x^5\cdot 3b+(3b)^2=(x^5-3b)^2$$
6. $$36m^6+n^{12}+12m^3n^6=36m^6+12m^3n^6+n^{12}=(6m^3)^2+2\cdot 6m^3\cdot n^6+(n^6)^2=(6m^3+n^6)^2$$
7. $$\frac{1}{196}x^8-2x^4y^2+196y^4=\left(\frac{1}{14}x^4\right)^2-2\cdot \frac{1}{14}x^4\cdot 14y^2+(14y^2)^2=\left(\frac{1}{14}x^4-14y^2\right)^2$$
8. $$\frac{81}{16}a^6-9a^3b^2+4b^4=\left(\frac{9}{4}a^3\right)^2-2\cdot \frac{9}{4}a^3\cdot 2b^2+(2b^2)^2=\left(\frac{9}{4}a^3-2b^2\right)^2$$

Ответ

1) $$(a-7)^2$$
2) $$(5y+1)^2$$
3) $$(10a-9b)^2$$
4) $$(4m-7n)^2$$
5) $$(x^5-3b)^2$$
6) $$(6m^3+n^6)^2$$
7) $$\left(\frac{1}{14}x^4-14y^2\right)^2$$
8) $$\left(\frac{9}{4}a^3-2b^2\right)^2$$