Question

Phân tích đa thức sau thành nhân tử

k) 125x³ - 1

m) x⁶ - y³ 

n) a⁴ - 2a² +1

l ) a³ + 6a² + 12a + 8

giúp mình với nhé mình cảm ơn nhiều ạ

Answer 1

k ) \(125x^3-1\)

     \(=\left(5x\right)^3-1\)

     \(=\left(5x-1\right)\left[\left(5x\right)^2+5x.1+1^2\right]\)

     \(=\left(5x-1\right)\left(25x^2+5x+1\right)\)

m ) \(x^6-y^3=\left(x^2\right)^3-y^3=\left(x^2-y\right).\left[\left(x^2\right)^2+x^2.y+y^2\right]=\left(x^2-y\right).\left(x^4+x^2y+y^2\right)\)

n ) \(a^4-2a^2+1\)

\(=\left(a^2\right)^2-2.a^2.1+1^2=\left(a^2-1\right)^2\)

i ) \(a^3+6a^2+12a+8\)

\(=\left(a+2\right)^3\)

Answer 2

k) \(125x^3-1=\left(5x\right)^3-1=\left(5x-1\right)\left(25x^2+5x+1\right)\)

m) \(x^6-y^3=\left(x^2\right)^3-y^3=\left(x^2-y\right)\left(x^4+x^2y+y^2\right)\)

n) \(a^4-2a^2+1=\left(a^2-1\right)^2=\left(a^2-1\right)\left(a^2-1\right)=\left(a-1\right)\left(a+1\right)\left(a-1\right)\left(a+1\right)\)

i) \(a^3+6a^2+12a+8=\left(a+2\right)^2\)