* a(b - c) - a(b + d) = -a(c + d)
Ta có:
VT = a (b - c) - a ( b + d)
= ab - ac - ab - ad
= ( ab - ab) - (ac + ad)
= - a(c + d) = VP (đpcm)
* (a + b)(c + d) - (a + d)(b + c) = (a - c)(d - b)
Ta có:
VT = (a + b)(c + d) - (a + d)(b + c)
= ac + ad + bc + bd - ( ab + ac + bd + cd)
= ac + ad + bc + bd - ab - ac - bd - cd
= (ac - ac) + (bd - bd) + (ad - cd) + (bc - ab)
= 0 + 0 + d(a - c) + b(c - a)
= d (a - c) - b (a - c)
= (a - c)(d - b) = VP (đpcm)
