Question

Phân tích đa thức thành nhân tử bằng phương pháp dùng hằng đẳng thức

1) 4a²b⁴ - c⁴d²

²⁾ 7x³ - a³b³

³⁾ 16³ + 54y⁴

4) (a+b)³ - (a-b)³

5) (a+b)³ + ( a-b)³

⁶⁾ (6x- 1)² - (3x + 2)

7) (3x-1)²- 16

8) (5x- 4)²-49x²

9) (3x+1)² - 4(x-2)²

10) (2x+5)² - (x-9)²

Answer 1

1: \(4a^2b^4-c^4d^2\)

\(=\left(2ab^2-c^2d\right)\left(2ab^2+c^2d\right)\)

4: \(\left(a+b\right)^3-\left(a-b\right)^3\)

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

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

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

5: \(\left(a+b\right)^3+\left(a-b\right)^3\)

\(=a^3+b^3+3a^2b+3ab^2+a^3-3a^2b+3ab^2-b^3\)

\(=2a^3+6ab^2\)

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