Question

1.chứng minh đẳng thức sau
(a+b)²-(a-b)(a+b)=2b(a+b)
2.rút gọn các biểu thức sau
a)A=(x-y)²+4xy      b)B=(6x-2)²+44(3x-1)(2+y)+(y+2)²
c)C=(x-y)²+2(x²-y2)+(x+y)²
 

Answer 1

1) \(VP=\left(a+b\right)\left[a+b-\left(a-b\right)\right]=2b\left(a+b\right)=VT\left(đpcm\right)\)

2) a. \(A=\left(x-y\right)^2+4xy=x^2-2xy+y^2+4xy=x^2+y^2+2xy=\left(x+y\right)^2\)

\(B=\left(6x-2\right)^2+44\left(3x-1\right)\left(2+y\right)+\left(y+2\right)^2=\left(6x-2+y+2\right)^2\)  = \(\left(6x+y\right)^2\)

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

\(=\left(x-y+x+y\right)^2=4x^2\)