Question

rút gọn về hàng đẳng thức:

a) (2x+1)²+2(2x+1)+1

b) (x-y)²+(x+y)²-2(x+y)(x-y)

Answer 1

a) \(\left(2x+1\right)^2+2\left(2x+1\right)+1\)

\(=\left(2x+1\right)^2+2\cdot\left(2x+1\right)\cdot1+1^2\)

\(=\left[\left(2x+1\right)+1\right]^2\)

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

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

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

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

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

\(=\left(-2y\right)^2\)

\(=4y^2\)