Question

Viết các đa thức dưới dạng bình phương 1 tổng (hiệu)

a)\(27^2+13^2+2.37.13\)

b)\(87^2+67^2-147.67\)

c)\(x^2-2xy+2y^2+2y+1\)

d)\(4x^2-12x-y^2+2y+1\)

Answer 1

a, \(27^2+13^2+2.37.13=\left(27+13\right)^2\)

b, \(87^2+57^2-174.67=\left(87-57\right)^2\)

c, \(x^2-2xy+2y^2+2y+1\)

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

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

d, \(4x^2-12x-y^2+2y+1\)

\(=4\left(x^2-3x\right)-\left(y^2-2y+1\right)+2\)

\(=4\left(x^2-\dfrac{3}{2}.x.2+\dfrac{9}{4}-\dfrac{9}{4}\right)-\left(y-1\right)^2+2\)

\(=\left(x-\dfrac{3}{2}\right)^2-\left(y-1\right)^2-7\)