Упр.132 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) a^2 + 8a + 16;
2) 9x^2 — 6x + 1;
3) 121m^2 — 88mn + 16n^2;
4) 24ab + 36a^2 + 4b^2;
5) a^6 — 4a^3 b + 4b^2;
6) 25p^10 + q^8 + 10p^5 q^4;
7) 1/169 x^4 + 2x^2 y^2 + 169y^4;
8) 9/64 n^6 + 3mn^5 + 16m^2 n^4.

1. $$a^2+8a+16=a^2+2\cdot a\cdot 4+4^2=(a+4)^2$$
2. $$9x^2-6x+1=(3x)^2-2\cdot 3x\cdot 1+1^2=(3x-1)^2$$
3. $$121m^2-88mn+16n^2=(11m)^2-2\cdot 11m\cdot 4n+(4n)^2=(11m-4n)^2$$
4. $$36a^2+24ab+4b^2=(6a)^2+2\cdot 6a\cdot 2b+(2b)^2=(6a+2b)^2$$
5. $$a^6-4a^3b+4b^2=(a^3)^2-2\cdot a^3\cdot 2b+(2b)^2=(a^3-2b)^2$$
6. $$25p^{10}+10p^5q^4+q^8=(5p^5)^2+2\cdot 5p^5\cdot q^4+(q^4)^2=(5p^5+q^4)^2$$
7. $$\frac{1}{169}x^4+2x^2y^2+169y^4=\left(\frac{1}{13}x^2\right)^2+2\cdot \frac{1}{13}x^2\cdot 13y^2+(13y^2)^2=\left(\frac{1}{13}x^2+13y^2\right)^2$$
8. $$\frac{9}{64}n^6+3mn^5+16m^2n^4=\left(\frac{3}{8}n^3\right)^2+2\cdot \frac{3}{8}n^3\cdot 4mn^2+(4mn^2)^2=\left(\frac{3}{8}n^3+4mn^2\right)^2$$

Ответ

1) $$(a+4)^2$$
2) $$(3x-1)^2$$
3) $$(11m-4n)^2$$
4) $$(6a+2b)^2$$
5) $$(a^3-2b)^2$$
6) $$(5p^5+q^4)^2$$
7) $$\left(\frac{1}{13}x^2+13y^2\right)^2$$
8) $$\left(\frac{3}{8}n^3+4mn^2\right)^2$$