Question

Phân tích đa thức thành nhân tử:

a) a²y² + b²x² - 2abxy

b) 100 - (3x - y)²

c) 27x³ - a³b³

d) (a + b)³ - (a - b)³

Answer 1

a) \(a^2y^2+b^2x^2-2abxy\)

\(=\left(ay\right)^2-2aybx+\left(bx\right)^2\)

\(=\left(ay-bx\right)^2\)

Answer 2

b) \(100-\left(3x-y\right)^2\)

\(=10^2-\left(3x-y\right)^2\)

\(=\left[10-\left(3x-y\right)\right].\left[10+\left(3x-y\right)\right]\)

\(=\left(10-3x+y\right)\left(10+3x-y\right)\)

Answer 3

c) \(27x^3-a^3b^3\)

\(=\left(3x\right)^3-\left(ab\right)^3\)

\(=\left(3x-ab\right)\left[\left(3x\right)^2+3xab+\left(ab\right)^2\right]\)

\(=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)

Answer 4

d) \(\left(a+b\right)^3-\left(a-b\right)^3\)

\(=\left[\left(a+b\right)-\left(a-b\right)\right]\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)

\(=\left(a+b-a+b\right)\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)\)

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