Question

[Nguyễn Minh Phúc]

Bài 1: Chứng tỏ 

a,  (a - b + c) - (a + c) = -b

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

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

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

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

Bài 2: Viết dưới dạng tích các tổng sau :

a,  ab + ac

b,  ab - ac + ad

c,  ax - bx - cx + dx

d,   a(b + c ) - d( b + c)

e,   ac - ad + bc - bd

g,   ax + by + bx + ay

Answer 1

[Dương]

\(a,\left(a-b+c\right)-\left(a+c\right)=-b\)

Ta có: \(VT=\left(a-b+c\right)-\left(a+c\right)=a-b+c-a-c=-b=VP\left(đpcm\right)\)

\(b,\left(a+b\right)-\left(b-a\right)+c=2a+c\)

Ta có: \(VT=\left(a+b\right)-\left(b-a\right)+c=a+b-b+a+c=2a+c=VP\left(đpcm\right)\)

\(c,-\left(a+b-c\right)+\left(a-b-c\right)=-2b\)

Ta có: \(VT=-\left(a+b-c\right)+\left(a-b-c\right)=-a-b+c+a-b-c=-2b=VP\left(đpcm\right)\)

\(d,a\left(b+c\right)-a\left(b+d\right)=a\left(c-d\right)\)

Ta có: \(VT=a\left(b+c\right)-a\left(b+d\right)=ab+ac-ab-ad=ac-ad=a\left(c-d\right)=VP\left(đpcm\right)\)

\(e,a\left(b-c\right)+a\left(d+c\right)=a\left(b+d\right)\)

Ta có: \(VT=a\left(b-c\right)+a\left(d+c\right)=ab-ac+ad+ac=ab+ad=a\left(b+d\right)=VP\left(đpcm\right)\)

Answer 2

[๛Ňɠũ Vị Čáէツ]

Bài 1: 

a,  (a - b + c) - (a + c) 

= a - b + c - a - c

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

= -b

b,   ( a + b ) - (b - a ) + c 

= a + b - b + a + c

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

= 2a + c

c,   - (  a + b - c) + (a - b -c) 

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

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

= - 2b

d,   a(b + c) - a ( b + d ) 

= ab + ac - ab - ad

= ac - ad

= a( c-d )

e,   a( b - c )  + a( d + c )

= ab - ac + ad + ac

= ab + ad

= a( b+d )

Bài 2: 

a,  ab + ac = a( b + c)

b,  ab - ac + ad= a( b -c + d )

c,  ax - bx - cx + dx = x( a - b - c + d)

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

e,   ac - ad + bc - bd = a ( c - d ) + b( c - d) = (a+b).( c - d )

g,   ax + by + bx + ay = a( x + y) + b(y + x) = ( a+b).( x+y )