Упр.132 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) a^2+10a+25; 5) m^8-6m^4 n^5+9n^10;
2) 4x^2-4x+1; 6) 36x^12+y^6+12x^6 y^3;
3) 64n^2-80nq+25q^2; 7) 1/225 a^6-2a^3 b^2+225b^4;
4) 80xy+16x^2+100y^2; 8) 25/49 a^4+10a^2 b^3+49b^6.

1. $$a^2+10a+25=a^2+2\cdot a\cdot 5+5^2=(a+5)^2$$
2. $$4x^2-4x+1=(2x)^2-2\cdot 2x\cdot 1+1^2=(2x-1)^2$$
3. $$64n^2-80nq+25q^2=(8n)^2-2\cdot 8n\cdot 5q+(5q)^2=(8n-5q)^2$$
4. $$80xy+16x^2+100y^2=16x^2+80xy+100y^2=(4x)^2+2\cdot 4x\cdot 10y+(10y)^2=(4x+10y)^2$$
5. $$m^8-6m^4n^5+9n^{10}=(m^4)^2-2\cdot m^4\cdot 3n^5+(3n^5)^2=(m^4-3n^5)^2$$
6. $$36x^{12}+y^6+12x^6y^3=36x^{12}+12x^6y^3+y^6=(6x^6)^2+2\cdot 6x^6\cdot y^3+(y^3)^2=(6x^6+y^3)^2$$
7. $$\frac{1}{225}a^6-2a^3b^2+225b^4=\left(\frac{1}{15}a^3\right)^2-2\cdot \frac{1}{15}a^3\cdot 15b^2+(15b^2)^2=\left(\frac{1}{15}a^3-15b^2\right)^2$$
8. $$\frac{25}{49}a^4+10a^2b^3+49b^6=\left(\frac{5}{7}a^2\right)^2+2\cdot \frac{5}{7}a^2\cdot 7b^3+(7b^3)^2=\left(\frac{5}{7}a^2+7b^3\right)^2$$

Ответ

1) $$(a+5)^2$$

2) $$(2x-1)^2$$

3) $$(8n-5q)^2$$

4) $$(4x+10y)^2$$

5) $$(m^4-3n^5)^2$$

6) $$(6x^6+y^3)^2$$

7) $$\left(\frac{1}{15}a^3-15b^2\right)^2$$

8) $$\left(\frac{5}{7}a^2+7b^3\right)^2$$