Представьте в виде многочлена выражение: 1) (x - 6)(x + 6); 2) (3 + x)(x - 3); 3) (3b - 5)(3b + 5); 4) (5x + 8y)(8y - 5x); 5) (m⁵ - n³)(m⁵ + n³); 6) (5a²b - 1/4 ab²)(5a²b + 1/4 ab²); 7) (0,5x³ + 0,2y⁴)(0,5x³ – 0,2y⁴); 8) (a⁵ - b⁵)(a⁵ + b⁵)(a¹⁰ + b¹⁰); 9) (-x⁷ - y³)(y³ - x⁷); 10) (2/3 y⁶ + 1,2x¹¹) (1,2x¹¹ - 2/3 y⁶).

Решение:

Используем формулу разности квадратов: (a - b)(a + b) = a² - b².

1. \( (x - 6)(x + 6) = x^2 - 6^2 = x^2 - 36 \)
2. \( (3 + x)(x - 3) = (x + 3)(x - 3) = x^2 - 3^2 = x^2 - 9 \)
3. \( (3b - 5)(3b + 5) = (3b)^2 - 5^2 = 9b^2 - 25 \)
4. \( (5x + 8y)(8y - 5x) = (8y + 5x)(8y - 5x) = (8y)^2 - (5x)^2 = 64y^2 - 25x^2 \)
5. \( (m^5 - n^3)(m^5 + n^3) = (m^5)^2 - (n^3)^2 = m^{10} - n^6 \)
6. \( (5a^2b - \frac{1}{4}ab^2)(5a^2b + \frac{1}{4}ab^2) = (5a^2b)^2 - (\frac{1}{4}ab^2)^2 = 25a^4b^2 - \frac{1}{16}a^2b^4 \)
7. \( (0.5x^3 + 0.2y^4)(0.5x^3 - 0.2y^4) = (0.5x^3)^2 - (0.2y^4)^2 = 0.25x^6 - 0.04y^8 \)
8. \( (a^5 - b^5)(a^5 + b^5)(a^{10} + b^{10}) = (a^{10} - b^{10})(a^{10} + b^{10}) = (a^{10})^2 - (b^{10})^2 = a^{20} - b^{20} \)
9. \( (-x^7 - y^3)(y^3 - x^7) = -(x^7 + y^3)(-(x^7 - y^3)) = (x^7 + y^3)(x^7 - y^3) = (x^7)^2 - (y^3)^2 = x^{14} - y^6 \)
10. \( (\frac{2}{3}y^6 + 1.2x^{11})(1.2x^{11} - \frac{2}{3}y^6) = (1.2x^{11} + \frac{2}{3}y^6)(1.2x^{11} - \frac{2}{3}y^6) = (1.2x^{11})^2 - (\frac{2}{3}y^6)^2 = 1.44x^{22} - \frac{4}{9}y^{12} \)