Question

[Kim Ngân Trương]

 

Answer 1

[Nguyễn Lê Phước Thịnh]

1: \(x^2-25=\left(x-5\right)\left(x+5\right)\)

2: \(9x^2-\dfrac{1}{16}y^2=\left(3x\right)^2-\left(\dfrac{1}{4}y\right)^2\)

\(=\left(3x-\dfrac{1}{4}y\right)\left(3x+\dfrac{1}{4}y\right)\)

3: \(x^6-y^4=\left(x^3\right)^2-\left(y^2\right)^2=\left(x^3-y^2\right)\left(x^3+y^2\right)\)

4: \(\left(2x-5\right)^2-64=\left(2x-5-8\right)\left(2x-5+8\right)\)

\(=\left(2x-13\right)\left(2x+3\right)\)

5: \(81-\left(3x+2\right)^2\)

\(=\left(9-3x-2\right)\left(9+3x+2\right)\)

\(=\left(-3x+7\right)\left(3x+11\right)\)

6: \(9\left(x-5y\right)^2-16\left(x+y\right)^2\)

\(=\left(3x-15y\right)^2-\left(4x+4y\right)^2\)

\(=\left(3x-15y-4x-4y\right)\left(3x-15y+4x+4y\right)\)

\(=\left(-x-19y\right)\left(7x-11y\right)\)

7: \(x^3-8=x^3-2^3=\left(x-2\right)\left(x^2+2x+4\right)\)

8: \(27x^3+125y^3=\left(3x\right)^3+\left(5y\right)^3\)

\(=\left(3x+5y\right)\left(9x^2-15xy+25y^2\right)\)

9: \(x^6+216=\left(x^2\right)^3+6^3\)

\(=\left(x^2+6\right)\left(x^4-6x^2+36\right)\)

10: \(x^2+8x+16=x^2+2\cdot x\cdot4+4^2=\left(x+4\right)^2\)

11: \(9x^2-12xy+4y^2\)

\(=\left(3x\right)^2-2\cdot3x\cdot2y+\left(2y\right)^2\)

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

12: \(-25x^2y^2+10xy-1\)

\(=-\left[\left(5xy\right)^2-2\cdot5xy\cdot1+1^2\right]\)

\(=-\left(5xy-1\right)^2\)

13: \(x^3-6x^2+12x-8\)

\(=x^3-3\cdot x^2\cdot2+3\cdot x\cdot2^2-2^3\)

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

14: \(8x^3+12x^2y+6xy^2+y^3\)

\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2+y^3\)

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