Вправа 599 алгебра Бевз гдз 7 клас

№ 599

а) 8 – (a – 2)³ = 2³ – (a – 2)² = (2 – a + 2)(4 + 2(a – 2) + (a – 2)²) =
= (4 – a)(4 + 2a – 4 + a² – 4a + 4) = (4 – a)(a² – 2a + 4);
б) (x + y)³ – y³ = (x + y – y)((x + y)² + (x + y)y + y²) =
= x(x² + 2xy + y² + xy + y² + y²) = x(x² + 3xy + 3y²);
в) (3 – 2x)³ + 8x³ = (3 – 2x + 2x)((3 – 2x)² – 2x(3 – 2x) + 4x²) =
= 3 • (12x² – 18x + 9);
г) (3 – a)³ – (a – 2)³ = (3 – a – a + 2)((3 – a)² + (3 – a)(a – 2) +
+ (a – 2))² = (5 – 2a)(9 – 6a + a² + 3a – 6 – a² + 2a + a² – 4a + 4) =
= (5 – 2a)(a² – 5a + 7).