ГДЗ до підручника «Алгебра» О.С. Істера. 7 клас

411. 1) a²b + a + ab² + b + 9ab + 9 = (a²b + a) + (ab² + b) + (9ab + 9) = a (ab + 1) + b(ab + 1) + 9(ab + 1) = (ab + 1)(a + b + 9));

2) 8ax + 4bx - 4x + 10am + 5bm - 5m = 4x(2a + b - 1) + 5m(2a + b - 1) = (4x + 5m)(2a + b - 1).

412. 1) x² + 5x + 4 = (x² + 4x) + (x + 4) = x(x + 4) + (x + 4) = (x + 4)(x + 1);

2) x² - 5x + 4 = (x² - 4x) + (4 - x) = x(x - 4) - (x - 4) = (x - 4)(x - 1);

3) x² + x - 6 = x² - 2x + 3x - 6 = x (x - 2) + 3(x - 2) = (x - 2)(x + 3);

4) a² + 4ab + 3b² = a² + 3ab + ab + 3b² = a(a + 3b) + b(a + 3b) = (a + 3b)(a + b).

413. 1) x² - 6x + 5 = x² - x - 5x + 5 = x(x - 1) - 5(x - 1) = (x - 1)(x - 5);

2) x² - x - 6 = x² - 2x + 3x - 6 = x(x - 2) + 3(x - 2) = (x - 2)(x + 3);

3) x² + 2x - 15 = (x² + 5x) + (-3x - 15) = x(x + 5) - 3(x + 5) = (x + 5)(x - 3);

4) a² + 5ab + 6b² = (a² + 3ab) + (2ab + 6b²) = a(a + 3b) + 2b(a + 3b) = (a + 3b)(a + 2b).