Вправи: 863

863. Подайте вираз у вигляді добутку:

1) a² – 81 + a – 9 = (a² – 9²) + (a – 9) = (a – 9)(a + 9) + (a – 9) = (a – 9)(a + 9 + 1) = (a – 9)(a + 10);

2) m² – a² – (a + m) = (m – a)(m + a) – (m + a) = (m + a)(m – a – 1);

3) x² – y² – x + y = (x² – y²) – (x – y) = (x – y)(x + y) – (x – y) = (x – y)(x + y – 1);

4) x + x² – y – y² =(x² – y²) + (x – y) = (x – y)(x + y) + (x – y) = (x – y)(x + y + 1);

5) a – 3b + a² – 9b² = (a – 3b) + (a² – 9b²) = (a – 3b) + (a – 3b)(a + 3b) = (a – 3b)(1 + a + 3b);

6) 16m² – 25n² – 4m – 5n = (16m² – 25n²) – (4m + 5n) = (4m – 5n)(4m + 5n) – (4m + 5n) = (4m + 5n)(4m – 5n – 1).