1. Преобразовать в многочлен: 1) \((a+7)^2\); 2) \((3x-4y)^2\); 3) \((m-6)(m+6)\); 4) \((5a+8b)(8b-5a)\); 5) \((x^2+9x)^2\); 6) \((10a^5-\frac12bc^2)(10a^5+\frac12bc^2)\).

1. \((a+7)^2=a^2+2\cdot a\cdot 7+7^2=a^2+14a+49\).
2. \((3x-4y)^2=(3x)^2-2\cdot3x\cdot4y+(4y)^2=9x^2-24xy+16y^2\).
3. \((m-6)(m+6)=m^2-6^2=m^2-36\).
4. \((5a+8b)(8b-5a)=(8b)^2-(5a)^2=64b^2-25a^2\).
5. \((x^2+9x)^2=(x^2)^2+2\cdot x^2\cdot9x+(9x)^2=x^4+18x^3+81x^2\).
6. \((10a^5-\frac12bc^2)(10a^5+\frac12bc^2)=(10a^5)^2-(\frac12bc^2)^2=100a^{10}-\frac14b^2c^4\).

Ответ: 1) \(a^2+14a+49\); 2) \(9x^2-24xy+16y^2\); 3) \(m^2-36\); 4) \(64b^2-25a^2\); 5) \(x^4+18x^3+81x^2\); 6) \(100a^{10}-\frac14b^2c^4\).