Question

Phân tích đa thức thành nhân tử:

a)4b - 6a²b + 8a -3ab²

b) 4-4y²+12xy - 9x²

c) x²- 3x - 10

d) 8y - 2y³ +8xy² - 8x²y

e) 4x²(x-3) + 9(3-x)

f) x⁴y⁴ + 64

Answer 1

a)

$4b-6a^2b+8a-3ab^2$

$=(4b-3ab^2)+(8a-6a^2b)$

$=b(4-3ab)+2a(4-3ab)=(b+2a)(4-3ab)$

b)

$4-4y^2+12xy-9x^2=4-(9x^2-12xy+4y^2)$

$=2^2-(3x-2y)^2=(2-3x+2y)(2+3x-2y)$

c)

$x^2-3x-10=x^2-5x+2x-10=x(x-5)+2(x-5)=(x+2)(x-5)$

Answer 2

d)

$8y-2y^3+8xy^2-8x^2y=2y(4-y^2+4xy-4x^2)$
$=2y[4-(4x^2-4xy+y^2)]=2y[2^2-(2x-y)^2]$

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

e)

$4x^2(x-3)+9(3-x)=4x^2(x-3)-9(x-3)=(x-3)(4x^2-9)=(x-3)[(2x)^2-3^2]$

$=(x-3)(2x-3)(2x+3)$

f)

$x^4y^4+64=(x^2y^2)^2+8^2=(x^2y^2)^2+2.x^2y^2.8+8^2-16x^2y^2$

$=(x^2y^2+8)^2-(4xy)^2=(x^2y^2+8-4xy)(x^2y^2+8+4xy)$