Question

CM các đẳng thức

a, (a+b)-(-a+b-c)+(c-a-b)=a-b+2c

b, a nhân (b-c)-a nhân (b+d)=-a nhân (c+d)

Answer 1

a,(a+b)-(-a+b-c)+(c-a-b)

=a+b+a-b+c+c-a-b

=(a+a-a)-(b+b-b)+2c

=a-b+2c

b, a.(b-c)-a.(b+d)

=a.b-a.c-a.b+a.d

=(a.b-a.b)+(-a.c+-a.d)

= 0 + -a.(c+d)

Answer 2

a, (a+b) - (-a+b-c)+(c-a-b) = a-b+2c

*Xét : (a+b) - (-a+b-c) + (c-a-b)

= a+b+a-b+c+c-a-b

= (a+a-a) - (b+b-b) + (c+c)

= a-b+2c

Vì a-b+2c = a-b+2c

\(\Rightarrow\)(a+b) - (-a+b-c) + (c-a-b) = a-b+2c

Vậy (a+b) - (-a+b-c) + (c-a-b) = a-b+2c

b, a(b-c)-a(b+d) = -a(c+d)

*Xét : a(b-c)-a(b+d)

= ab-ac-ab+ad

= (ab-ab) + [-ac+(-ad)]

= 0 + (-a).(c+d)

= -a(c+d)

Vì -a(c+d) = -a(c+d)

\(\Rightarrow\)a(b-c)-a(b+d) = -a(c+d)

Vậy a(b-c)-a(b+d) = -a(c+d)

Answer 3

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