Question

Thu gọn biểu thức: 

a)x.(y-z)-z.(y-x)

b)(x+y).(x-y)

c)(x+y)\(^2\)-(x-y)\(^2\)

Giúp mik giải nha khẩn cấp lắm rùi nè

Answer 1

\(x\left(y-z\right)-z\left(y-x\right)\)

\(=xy-xz-zy+zx\)

\(=xy-zy=y\left(x-z\right)\)

\(\left(x+y\right)\left(x-y\right)\)

\(=x^2-xy+xy-y^2=x^2-y^2\)

\(\left(x+y\right)^2-\left(x-y\right)^2\)

\(=\left(x+y-x+y\right)\left(x+y+x-y\right)\)

\(=2y+2x=2\left(x+y\right)\)

Answer 2

a, x(y-z)-z(y-x)=xy-xz-zy+xz

                     =xy-zy=y(x-z)

b,(x+y)(x-y)=x²-y²

c,(x+y)²-(x-y)²=(x+y+x-y)(x+y-x+y)

                     =2x.2y

                    =4xy

Answer 3

a) x.(y-z)-z.(y-x) = (xy-xz)-(zy-zx)=xy-xz-zy+zx=xy-zy=y.(x-z)

b)(x+y).(x-y)=(x^2-xy)+(yx-y^2)=x^2-xy+yx-y^2=x^2-y^2

c)(x+y)^2 - (x-y)^2 = (x+y).(x+y) - (x-y).(x-y)=[(x^2+xy)+(yx+y^2)] - [(x^2-xy)-(yx-y^2]=(x^2+xy+yx+y^2)-(x^2-xy-yx+y^2)

=x^2+xy+yx+y^2-x^2+xy+yx-y^2=xy+yx+xy+yx = 4xy

k mình nha!