Question

Rút gọn biểu thức sau:

a.) (a+b)²-(a-b)²

b.) (a+b)³-(a-b)³-2b³

c.) (x+y+z)²-2(x+y+z)(x+y)+(x+y)²

Answer 1

a)

\(\left(a+b\right)^2-\left(a-b\right)^2=\left(a+b+a-b\right)\left(a+b-a+b\right)\\ =2a.2b=4ab\)

b)

\(\left(a+b\right)^3-\left(a-b\right)^3-2b^3\\ =\left(a+b-a+b\right)\left[\left(a+b\right)^2+a^2-b^2+\left(a-b\right)^2\right]-2b^3\\ =2b\left(3a^2+b^2-b^2\right)=2b.3a^2=6a^2b\)

c)

\(\left(x+y+z\right)^2-2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\\ =\left[\left(x+y+z\right)-\left(x+y\right)\right]^2\\ =\left(x+y+z-x-y\right)^2=z^2\)