Question

Phân tích các đa thức thành nhân tử:

a) 9x² + 24xy + 16y²

b) 8x³ + 1

c) a⁴ - b⁴

d) (a² + 9)² - 36a²

Answer 1

a/ \(9x^2+24xy+16y^2=\left(3x\right)^2+2\cdot3x\cdot4y+\left(4y\right)^2=\left(3x+4y\right)^2\)

b/ \(8x^3+1=\left(2x\right)^3+1^3=\left(2x+1\right)\left(4x^2+2x+1\right)\)

c/ \(a^4-b^4=\left(a^2-b^2\right)\left(a^2+b^2\right)=\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)\)

d/ \(\left(a^2+9\right)^2-36a^2=\left(a^2+9-6a\right)\left(a^2+9+6a\right)=\left(a-3\right)^2\cdot\left(a+3\right)^2=\left[\left(a-3\right)\left(a+3\right)\right]^2=\left(a^2-9\right)^2\)