Question

Phân tích đa thức thành nhân tử:

a, 3x² - 4y + 4y - 3y²

b, (4x² - 7x - 50)² - 16x⁴ - 56x³ - 49x²

c, (x² - y² - 5)² - 4x²y² - 16xy - 16

d, x⁶ + 3x⁴y² - 8x³y³ + 3x²y⁴ + y⁶

Answer 1

a: \(=3x^2-3y^2=3\left(x-y\right)\left(x+y\right)\)

b: \(=\left(4x^2-7x-50\right)^2-\left(16x^4+56x^3+49x^2\right)\)

\(=\left(4x^2-7x-50\right)^2-\left(4x^2+7x\right)^2\)

\(=\left(4x^2-7x-50-4x^2-7x\right)\left(4x^2-7x-50+4x^2+7x\right)\)

\(=\left(-14x-50\right)\left(8x^2-50\right)\)

\(=-4\left(7x+25\right)\left(2x-5\right)\left(2x+5\right)\)

d: \(=\left(x^2+y^2\right)^3-8x^3y^3\)

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

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