Question

Даю 42 балла. упростите выражение: 1) P+Q,если Р=5а²+b,Q=-4a²-b 2) P-Q, если P=2p²-3q³, Q=2p²-4q³ 3) A+B+C, если A = a² - b² + ab B=2a²+3ab-5b², C = -4a² + 2ab - 3b² 4) A-B+C, если A=2a² - 3ab + 4ab² B = 3a²+4ab-b², C = a²+2ab-3b²

Answer 1

Ответ:

1) 5a² +b-4a²-b=a²

2) 2p²-3q³-2p²+4q³=q³

3) a²-b²+ab+2a²+3ab-5b²-4a²+2ab-3b²=-a²-9b²+6ab

4) 2a²-3ab+4ab²-3a²-4ab+b²+a²+2ab-3b²=-5ab+4ab²-2b²

Answer 2

1. P + Q: Given P = 5a² + b and Q = -4a² - b, we can simplify the expression: P + Q = (5a² + b) + (-4a² - b) = 5a² - 4a² + b - b = a²

   Therefore, the simplified expression for P + Q is a².

2. P - Q: Given P = 2p² - 3q³ and Q = 2p² - 4q³, we can simplify the expression: P - Q = (2p² - 3q³) - (2p² - 4q³) = 2p² - 3q³ - 2p² + 4q³ = -3q³ + 4q³ = q³

   Therefore, the simplified expression for P - Q is q³.

3. A + B + C: Given A = a² - b² + ab, B = 2a² + 3ab - 5b², and C = -4a² + 2ab - 3b², we can simplify the expression: A + B + C = (a² - b² + ab) + (2a² + 3ab - 5b²) + (-4a² + 2ab - 3b²) = a² + 2a² - 4a² - b² + 3ab + 2ab - 5b² - 3b² = (a² + 2a² - 4a²) + (-b² - 5b² - 3b²) + (3ab + 2ab) = -a² - 9b² + 5ab

   Therefore, the simplified expression for A + B + C is -a² - 9b² + 5ab.

4. A - B + C: Given A = 2a² - 3ab + 4ab², B = 3a² + 4ab - b², and C = a² + 2ab - 3b², we can simplify the expression: A - B + C = (2a² - 3ab + 4ab²) - (3a² + 4ab - b²) + (a² + 2ab - 3b²) = 2a² - 3ab + 4ab² - 3a² - 4ab + b² + a² + 2ab - 3b² = (2a² - 3a² + a²) + (-3ab - 4ab + 2ab) + (4ab² + b² - 3b²) = 0a² - 5ab + ab + 4ab² + b² - 3b² = -5ab + ab + 4ab² + b² - 3b² = -4ab + ab + 4ab² - 2b² = -3ab + 4ab² - 2b²

   Therefore, the simplified expression for A - B + C is -3ab + 4ab² - 2b².