Вправа 455 алгебра Бевз гдз 7 клас

№ 455

а) az² – bz² – bz + az – a + b = (az² + az – a) – (bz² + bz – b) =
= a(z² + z – 1) – b(z² + z – 1) = (z² + z – 1)(a – b);
б) x² + 2x – ca – 2c – cx + ax = (x² + 2x + ax) – (ca + 2c + cx) =
= x(x + 2 + a) – c(a + 2 + x) = (x + 2 + a)(x – c);
в) x⁴ – a⁴ + a³x – ax³ + c³x – ac³ = (x⁴ – ax³) + (–a⁴ + a³x) +
+ (c³x – ac³) = x³(x – a) + a³(x – a) + c³(x – a) = (x – a)(x³ + a³ + c³);
г) a³ – a² + x³ – x² + a²x + ax² = (a³ – a² + a²x) + (x³ – x² + ax²) =
= a²(a – 1 + x) + x²(x – 1 + a) = (a – 1 + x)(a² + x²);
ґ) x³ + y³ + xy² + x²y + x²z + y²z = (x³ + x²y + x²z) + (y² + xy² +
+ y²z) = x²(x + y + z) + y²(x + y + z) = (x + y + z)(x² + y²);
д) a³ + a + ab² – a²b – b – b³ = (a3 + a + ab²) – (a²b + b + b²) =
= a(a² + 1 + b²) – b(a² + 1 + b)² = (a² + 1 + b²)(a – b).