Question

Answer 1

Câu 1:

a. x⁴ - 9x²y²

= (x²)² - (3xy)²

= (x² - 3xy)(x² + 3xy)

b. x² + 2xy + y² - 2x - 2y

= (x + y)² - 2(x + y)

= (x + y - 2)(x + y)

c. x⁴ + 4y²

= (x²)² + (2y)²

= (x² - 2y)(x² + 2y)

Answer 2

Câu 2:

a) \(A=x^2+5x+8=\left(x^2+5x+\dfrac{25}{4}\right)+\dfrac{7}{4}=\left(x+\dfrac{5}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\)

\(minA=\dfrac{7}{4}\Leftrightarrow x=-\dfrac{5}{2}\)

b) \(B=x\left(x-6\right)=x^2-6x=\left(x^2-6x+9\right)-9=\left(x-3\right)^2-9\ge-9\)

\(minB=-9\Leftrightarrow x=3\)

Answer 3

Câu 1:

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

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

e) \(=\left(x-2\right)^3-\left(x-2\right)=\left(x-2\right)\left[\left(x-2\right)^2-1\right]=\left(x-2\right)\left(x-2-1\right)\left(x-2+1\right)=\left(x-2\right)\left(x-3\right)\left(x-1\right)\)

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

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

h) \(=\left(x-y\right)\left(x+y\right)+5\left(x-y\right)=\left(x-y\right)\left(x+y+5\right)\)