5-1

1.      Tegurda.

a)     a(x – y) + x – y

Lahendus: a(x – y) + x – y = a(x – y) + (x – y) =

= (a + 1)(x – y)

b)     a + b + x(a + b)

Lahendus: a + b + x(a + b) = (a + b) + x(a + b) =

                        = (1 + x)(a + b)

c)      x(a – b) + y(a – b)

Lahendus: x(a – b) + y(a – b) = (x + y)(a – b)

d)     a(b – c) – k(b – c)

Lahendus: a(b – c) – k(b – c) = (a – k)(b – c)

e)     2a(x + y) – x – y

Lahendus: 2a(x + y) – x – y = 2a(x + y) – (x + y) =

                        = (2a – 1)(x + y)

f)       a(m – n) + bm – bn

Lahendus: a(m – n) + bm – bn = a(m – n) + b(m – n) =

                        = (a + b)(m – n)

2.      Tegurda.

a)     ax + ay – bx – by

Lahendus: ax + ay – bx – by = (ax + ay) + (– bx – by) =

                        = a(x + y) – b(x + y) = (a – b)(x + y)

b)     ac – bc + ad – bd

Lahendus: ac – bc + ad – bd = (ac – bc) + (ad – bd) =

                        = c(a – b) + d(a – b) = (c + d)(a – b)

c)      ay + 2bx + 2ax + by

Lahendus: ay + 2bx + 2ax + by = (ay + by) + (2bx + 2ax) =

                        = y(a + b) + 2x(a + b) = (2x + y)(a + b)

d)     ac + 3bx + 3ax + bc

Lahendus: ac – 3bx – 3ax + bc = (ac + bc) + (– 3bx – 3ax) =

                        = c(a + b) – 3x(a + b) = (c – 3x)(a + b)

e)     10ax – 5bx + 2ay – by

Lahendus: 10ax – 5bx + 2ay – by = (10ax – 5bx) + (2ay – by) =

                        = 5x(2a – b) + y(2a – b) = (5x + y)(2a – b)

f)       5ax – 4by – 4ay + 5bx

Lahendus: 5ax – 4by – 4ay + 5bx = (5ax + 5bx) + (– 4by – 4ay) =

                        = 5x(a + b) – 4y(a + b) = (5x – 4y)(a + b)

g)     b³ – ab² + a²b – a³

Lahendus: b³ – ab² + a²b – a³ = (b³ – ab²) + (a²b – a³) =

                        = b²(b – a) + a²(b – a) = (a² + b²)(b – a)

h)     a³ + a²c – ac² – c³

Lahendus: a³ + a²c – ac² – c³ = (a³ + a²c) + (– ac² – c³) =

                        = a²(a + c) – c²(a + c) = (a² – c²)(a + c)

printerisõbralik versioon esita küsimus