Question

Rút gọn biểu thức:
a) A = (x + y)^2 – (x – y)^2
b) B = (x +2)^2 + 2.(x + 2).(x - 3) +( x - 3)^2
c) C = (x +2)^2 - 2.(x + 2).(x + 3) +( x + 3)^2

Answer 1

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

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

\(b.B=\left(x+2\right)^2+2\left(x+2\right)\left(x-3\right)+\left(x-3\right)^2\)

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

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

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

\(c.C=\left(x+2\right)^2-2\left(x+2\right)\left(x+3\right)+\left(x+3\right)^2\)

\(=x^2+4x+4-2x^2-10x-12+x^2+6x+9\)

\(=x^2-2x^2+x^2+4x-10x+6x+4-12+9\)

\(=1.\)