Question

1. Спростіть вираз 1) (3m + 5n) + (9m - 7n) - (-2n + 5m); 2) (12ab - b²) - (bab + b) + (ab + 2b²); 3) (3x² + 2x) + (2x²-3x-4)-(17-x²); 4) (m - n + p) + (m-p) - (m - n - p).​

Answer 1

1) (3m + 5n) + (9m - 7n) - (-2n + 5m) = 3m + 5n + 9m - 7n + 2n - 5m = (3m + 9m - 5m) + (5n - 7n + 2n) = 7m + 0n = 7m.

2) (12ab - b²) - (bab + b) + (ab + 2b²) = 12ab - b² - bab - b + ab + 2b² = 12ab - bab + ab - b² + 2b² - b = 12ab - bab + ab - b² + 2b² - b = 12ab - bab + ab - b = (12ab - bab + ab) - b = (12ab + ab - bab) - b = 13ab - bab - b.

3) (3x² + 2x) + (2x² - 3x - 4) - (17 - x²) = 3x² + 2x + 2x² - 3x - 4 - 17 + x² = (3x² + 2x² + x²) + (2x - 3x) - 4 - 17 = 6x² - x - 21.

4) (m - n + p) + (m - p) - (m - n - p) = m - n + p + m - p - m + n + p = (m + m - m) + (-n + n) + (p - p + p) = 0 + 0 + 2p = 2p.

Answer 2

1. (3m + 5n) + (9m - 7n) - (-2n + 5m) = 3m + 5n + 9m - 7n + 2n - 5m (Distribute the negative sign) = (3m + 9m - 5m) + (5n - 7n + 2n) (Group like terms together) = 7m + 0n = 7m

2. (12ab - b²) - (bab + b) + (ab + 2b²) = 12ab - b² - (bab + b) + ab + 2b² (Distribute the negative sign) = 12ab - b² - bab - b + ab + 2b² (Remove parentheses) = 12ab - bab + ab - b² + 2b² - b (Rearrange terms) = (12ab - bab + ab) + (2b² - b² - b) (Group like terms together) = ab(12 - ba + 1) + b²(2 - 1) (Factor out common terms) = ab(13 - ba) + b²(1) = ab(13 - ba) + b²

3. (3x² + 2x) + (2x² - 3x - 4) - (17 - x²) = 3x² + 2x + 2x² - 3x - 4 - 17 + x² (Remove parentheses) = (3x² + 2x² + x²) + (2x - 3x) - 4 - 17 (Group like terms together) = 6x² - x - 21

4. (m - n + p) + (m - p) - (m - n - p) = m - n + p + m - p - m + n + p (Remove parentheses) = (m + m - m) + (-n - p + n + p) (Group like terms together) = m + 0n = m