Преобразуйте выражение в многочлен: 16. a² + (2a-c)² 17. (5t+7z)²-70tz 18. 16b² - (a-4b)² 19. (d+7)·d + (1-d)² 20. 4(x-3)² - 2x(1+x)² 21. -(3x-y)²

Question

Accepted Answer

\( a^2 + (2a-c)^2 = a^2 + (4a^2 - 4ac + c^2) = 5a^2 - 4ac + c^2 \)
\( (5t+7z)^2 - 70tz = (25t^2 + 70tz + 49z^2) - 70tz = 25t^2 + 49z^2 \)
\( 16b^2 - (a-4b)^2 = 16b^2 - (a^2 - 8ab + 16b^2) = 16b^2 - a^2 + 8ab - 16b^2 = 8ab - a^2 \)
\( (d+7) \cdot d + (1-d)^2 = d^2 + 7d + (1 - 2d + d^2) = d^2 + 7d + 1 - 2d + d^2 = 2d^2 + 5d + 1 \)
\( 4(x-3)^2 - 2x(1+x)^2 = 4(x^2 - 6x + 9) - 2x(1 + 2x + x^2) = (4x^2 - 24x + 36) - (2x + 4x^2 + 2x^3) = 4x^2 - 24x + 36 - 2x - 4x^2 - 2x^3 = -2x^3 - 26x + 36 \)
\( -(3x-y)^2 = -(9x^2 - 6xy + y^2) = -9x^2 + 6xy - y^2 \)

Ответ: 1. 5a² - 4ac + c²; 2. 25t² + 49z²; 3. 8ab - a²; 4. 2d² + 5d + 1; 5. -2x³ - 26x + 36; 6. -9x² + 6xy - y².