Вправи: 571

571. Спростіть вираз:

1) а² + (3а – b)² = а² + 9а² – 6аb + b² = 10а² – 6аb + b²;

2) (4х + 5)² – 40х = 16х² + 40х + 25 – 40х = 16х² + 25;

3) 50а² – (7а – 1)² = 50а² – (49а² – 14а + 1) = 50а² – 49а² + 14а – 1 = а² + 14а – 1;

4) с² + 36 – (с – 6)² = с² + 36 – (с² – 12с + 36) = с² + 36 – с² + 12с – 36 = 12с;

5) (х – 2)² + х(х + 10) = х² – 4х + 4 + х² + 10х = 2x² + 6х + 4;

6) 3m(m – 4) – (m + 2)² = 3m² – 12m – (m² + 4m + 4) = 3m² – 12m – m² – 4m – 4 = 2m² – 16m – 4 ;

7) (y – 9)² + (4 – y)(y + 6) = y² – 18y + 81 + 4y + 24 – y² – 6y =

= –20y + 105;

8) (x –4)(x + 4) – (x – 1)² = x² – 16 – (x² – 2x + 1) = x² – 16 – x² + 2x – 1 = 2x – 17;

9) (2a – 3b)² + (3a + 2b)² = 4a² – 12ab + 9b² + 9a² + 12ab + 4b² =

= 13a² + 13b²;

10) (x – 5)² – (x – 7)(x + 7) = x² – 10x + 25 – (x² – 49) = x² – 10x + 25 – x² + 49 = –10x + 74.