Question

Phân tích nhân tử

a)  -4x² + 12xy - 9y² + 25

b) x³ - 3x² + 3x - 1

c) a⁶ - a⁴ + 2a³ + 2a²

Answer 1

bạn áp dụng các hằng đẳng thức là Ok:

a) \(-4x^2+12xy-9y^2+25=-\left(2x\right)^2+2.2x.3y-\left(3y\right)^2+25\)

= \(-\left(2x-3y\right)^2+25=\left(5-2x+3y\right)\left(5+2x-3y\right)\)

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

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

c) \(a^6-a^4+2a^3+2a^2=a^2\left(a^4-a^2+2a+2\right)=a^2\left[a^2\left(a^2-1\right)+2\left(a+1\right)\right]\)

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