\(a,x^2+y^2+2x+2y+2\left(x+1\right)\left(y+1\right)+2\)
\(=\left(x^2+2x+1\right)+2\left(x+1\right)\left(y+1\right)+\left(y^2+2y+1\right)\)
\(=\left(x+1\right)^2+2\left(x+1\right)\left(y+1\right)+\left(y+1\right)^2\)
\(=\left(x+1+y+1\right)^2\)
\(=\left(x+y+2\right)^2\)
\(---\)
\(b,x^2+2x\left(y+1\right)+y^2+2y+1\)
\(=x^2+2x\left(y+1\right)+\left(y^2+2y+1\right)\)
\(=x^2+2x\left(y+1\right)+\left(y+1\right)^2\)
\(=\left(x+y+1\right)^2\)
\(---\)
\(c,x^2-2x\left(y+2\right)+y^2+4y+4\)
\(=x^2-2x\left(y+2\right)+\left(y^2+4y+4\right)\)
\(=x^2-2x\left(y+2\right)+\left(y+2\right)^2\)
\(=\left[x-\left(y+2\right)\right]^2\)
\(=\left(x-y-2\right)^2\)
\(---\)
\(d,\left(x+3\right)\left(x+4\right)\left(x+5\right)\left(x+6\right)+1\)
\(=\left[\left(x+3\right)\left(x+6\right)\right]\cdot\left[\left(x+4\right)\left(x+5\right)\right]+1\)
\(=\left(x^2+3x+6x+18\right)\left(x^2+4x+5x+20\right)+1\)
\(=\left(x^2+9x+18\right)\left(x^2+9x+20\right)+1\) (1)
Đặt \(y=x^2+9x+18\)
Khi đó, (1) trở thành:
\(y\left(y+2\right)+1\)
\(=y^2+2y+1\)
\(=\left(y+1\right)^2\)
\(=\left(x^2+9x+18+1\right)^2\)
\(=\left(x^2+9x+19\right)^2\)
\(---\)
Cách làm: Nhóm các hạng tử để xuất hiện các HĐT số 1, 2 rồi áp dụng HĐT đó.
#\(Toru\)
