Question

1.Làm tính nhân:

a)x²(5x³-x-6)

b)(x²-2xy+y²)(x-y)

2.Viết các đa thức dưới dạng bình phương của 1 tổng hay 1 hiệu:

a)y²+2y+1

b)9x²+y²-6xy

c)25a²+4b²+20ab

d)x²-x+^{\(\dfrac{1}{4}\)}

Answer 1

Bài 1:

a) \(x^2\left(5x^3-x-6\right)\)

\(=x^2.5x^3-x^2.x-x^2.6\)

\(=5x^5-x^3-6x^2\)

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

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

\(=x^3-x^2y-2x^2y+2xy^2+y^2x-y^3\)

\(=x^3-3x^2y+3xy^2-y^3\)

Bài 2:

a) \(y^2+2y+1\)

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

b) \(9x^2+y^2-6xy\)

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

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

c) \(25a^2+4b^2+20ab\)

\(=\left(5a\right)^2+2.5a.2b+\left(2b\right)^2\)

\(=\left(5a+2b\right)^2\)

d) \(x^2-x+\dfrac{1}{4}\)

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

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