Question

1.(x+4)(x-5)+(3-x)= 2.10xy-5y+5(x-y)^2= 3.49-b^2= 4.x^3-1= 5.c^4-196= 6.m^3+n^3= 7.(x+y+c)(x-y+c)= 8.(a+1)^(a-1)^3= 9.(x-y)+b(x-y)^2+c(x-y)^3=(x- ^ - степень

Answer 1

1. (x + 4)(x — 5) + (3 — x) = x² — 5x + 4x — 20 + 3 — x = x² — 2x — 17 = x² — 2x + 1² — 18 = (x — 1)² — 18;

2. 10xy — 5y + 5 * (x — y)² = 10xy — 5y + 5 * (x² — 2xy + y²) =
10xy — 5y + 5x² — 10xy + 5y² = 5x² + 5y² — 5y =
5 * (x² + y² — y) = 5 * (x² + y * (y — 1));

3. 49 — b² = 7² — b² = (7 — b)(7 + b);

4. x³ — 1 = x³ — 1³ = (x — 1)(x² + x + 1);

5. c⁴ — 196 = c⁴ — 14² = (c²)² — 14² = (c² — 14)(c² + 14);

6. m³ + n³ = (m + n)(m² — mn + n²);

7. (x + y + c)(x — y + c) =
x² — xy + xc + xy — y² + cy + xc — cy + c² =
x² — y² + c² — xy + xy — cy + cy + xc + xc =
x² — y² + c² + 2xc = (x² + 2xc + c²) — y² =
(x + c)² — y² = (x + c — y)(x + c + y);

8. (a + 1)³ — (a — 1)³ = (a + 1 — a + 1)((a + 1)² — (a + 1)(a — 1) + (a — 1)²) = 
2 * (a² + 2a + 1 — a² + 1 + a² — 2a + 1) = 
2 * (a² + a² — a² + 2a — 2a + 1 + 1 + 1) = 
2 * (a² + 3) = 2a² + 6;

9. (x — y) + b * (x — y)² + c * (x — y)³ =
(x — y)(1 + b * (x — y) + c * (x — y)²) =
(x — y)(1 + (x — y)(b + c * (x — y))) =
(x — y)(1 + (x — y)(b + xc — cy))