Question

phân tích đa thức sau thành nhân tử :

(3x+1)^2 - 4(x - 2 )^2

9(2x+3)^2 - 4(x+1)^2

8x^3 - 64

x^6 - y^6

(x+y)^3 - (x - y )^3

Answer 1

\(\left(3x+1\right)^2-4\left(x-2\right)^2=9x^2+6x+1-4\left(x^2-4x+4\right)=9x^2+6x+1-4x^2+16x-16=5x^2+22x-15=\)

\(\left(5x-3\right)\left(x+5\right)\)

Answer 2

\(9\left(2x+3\right)^2-4\left(x+1\right)^2=9\left(4x^2+12x+9\right)-4\left(x^2+2x+1\right)=36x^2+108x+81-4x^2-8x-4=32x^2+100x+77\)

\(\left(8x+11\right)\left(4x+7\right)\)

Answer 3

\(8x^3-64=\left(2x\right)^3-4^3=\left(2x-4\right)\left(4x^2+8x+16\right)\)

Answer 4

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

Answer 5

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