Question

Áp dụng hằng đẳng thức, khai triển các biểu thức sau:

a, \(\left(2x+y+3\right)^2\)

b, \(\left(x-2y+1\right)^2\)

c, \(\left(x^2-2xy^2-3\right)^2\)

Answer 1

Giải:

a) \(\left(2x+y+3\right)^2\)

\(=\left(2x+y\right)^2+2.3\left(2x+y\right)+3^2\)

\(=\left(2x\right)^2+2.2x.y+y^2+2.3\left(2x+y\right)+3^2\)

\(=4x^2+4xy+y^2+12x+6y+9\)

Vậy ...

b) \(\left(x-2y+1\right)^2\)

\(=\left(x-2y\right)^2+2\left(x-2y\right)+1^2\)

\(=x^2-2.x.2y+\left(2y\right)^2+2x-4y+1^2\)

\(=x^2-4xy+4y^2+2x-4y+1\)

Vậy ...

c) \(\left(x^2-2xy^2-3\right)^2\)

\(=\left(x^2-2xy^2\right)^2+2.3.\left(x^2-2xy^2\right)-3^2\)

\(=\left(x^2\right)^2-2.x^2.2xy^2+\left(2xy^2\right)^2+2.3.\left(x^2-2xy^2\right)-3^2\)

\(=x^4-4x^3y^2+4x^2y^4+6x^2-12xy^2-9\)

Vậy ...