Ta có : 5x(x - 2y) + 2(2y - x)²

= 5x(x - 2y) + 2(x - 2y)² (vì (2y - x)² = (x - 2y)² )

= (x - 2y)[5x + 2(x - 2y)]

= (x - 2y)(5x + 2x - 4y)

= (x - 2y)(7x - 4y)

b) 7x(y - 4)² - (4 - y)³ 

= 7x(y - 4)² - (4 - y)²(4 - y)

= 7x(y - 4)² - (y - 4)²(4 - y)

= (y - 4)²(7x - 4 + y)

c) (4x - 8)(x² + 6) - (4x - 8)(x + 7) + 9(8 - 4x)

= (4x - 8)(x² + 6) - (4x - 8)(x + 7) - 9(4x - 8)

= (4x - 8)(x² + 6 - x - 7 - 9)

= 2(x - 4)(x² - x - 10)

Cưu là mình vs (x^2+x)^2-2(x^2+x)-15

a) 15x²-5x³=5x²(3-x)

a: \(15x^2-5x^3=5x^2\left(3-x\right)\)

b: \(8x^3-y^3+4x^2y-2xy^2\)

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

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

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

c: Ta có: \(x^8+64y^4\)

\(=x^8+16x^4y^2+64y^4-16x^4y^2\)

\(=\left(x^4+8y^2\right)^2-\left(4x^2y\right)^2\)

\(=\left(x^2-4x^2y+8y^2\right)\left(x^2+4x^2y+8y^2\right)\)

a) x² + 6x + 8

= x² + 2x + 4x + 8

= (x² + 2x) + (4x + 8)

= x(x + 2) + 4(x + 8)

= (x + 2)(x + 4)

b) 3x² - 2(x - y)² - 3y²

= (3x² - 3y²) - 2(x - y)²

= 3(x² - y²) - 2(x - y)²

= 3(x + y)(x - y) - 2(x - y)²

= (x - y)[3(x + y) - 2(x - y)]

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

= (x - y)(x + 5y)

c) 4x² - 9y² + 4x - 6y

= (4x² - 9y²) + (4x - 6y)

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

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

d) x(x + 1)² + x(x - 5) - 5(x + 1)²

= [x(x + 1)² - 5(x + 1)²] + x(x - 5)

= (x + 1)²(x - 5) + x(x - 5)

= (x - 5)[(x + 1)² + x]

= (x - 5)(x² + 2x + 1 + x)

= (x - 5)(x² + 3x + 1)

e) 2xy - x² + 3y² - 4y + 1

= -x² + 2xy - y² + 4y² - 4y + 1

= -(x² - 2xy + y²) + (4y² - 4y + 1)

= -(x - y)² + (2y - 1)²

= (2y - 1)² - (x - y)²

= (2y - 1 - x + y)(2y - 1 + x - y)

= (3y - x - 1)(x + y - 1)

f) 4x¹⁶ + 81

= (2x⁸)² + 2.2x⁸.9 + 9² - 2.2x⁸.9

= (2x⁸ + 9)² - 36x⁸

= (2x⁸ + 9) - (6x⁴)²

= (2x⁸ + 9 - 6x⁴)(2x⁸ + 9 + 6x⁴)

= (2x⁸ - 6x⁴ + 9)(2x⁸ + 6x⁴ + 9)

a: Ta có: \(x^2-6x+9-y^2\)

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

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

b: Ta có: \(x^3+4x^2+4x\)

\(=x\left(x^2+4x+4\right)\)

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

c: Ta có: \(4xy-4x^2-y^2+9\)

\(=-\left(4x^2-4xy+y^2-9\right)\)

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

1: \(3x\left(x-1\right)+7x^2\left(x-1\right)\)

\(=\left(x-1\right)\left(7x^2+3x\right)\)

=x(7x+3)(x-1)

2: \(9\left(x+5\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

=(3x+15+x-7)(3x+15-x+7)

=(4x+8)(2x+22)

\(=4\left(x+2\right)\cdot2\cdot\left(x+11\right)=8\left(x+2\right)\left(x+11\right)\)

3: \(x^2-2xy+y^2-xz+yz\)

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

=(x-y)(x-y-z)

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

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

\(=\left(x^2+2x-3\right)\left(x^2+2x+1\right)=\left(x+3\right)\left(x-1\right)\left(x+1\right)^2\)

5: \(9x^2y^2+15x^2y-21xy^2\)

\(=3xy\cdot3xy+3xy\cdot5x-3xy\cdot7y\)

=3xy(3xy+5x-7y)

6: \(x^3-2x^2y+xy^2-9xy^4\)

\(=x\left(x^2-2xy+y^2-9y^4\right)\)

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

7: \(x^2+x-12\)

\(=x^2+4x-3x-12\)

=x(x+4)-3(x+4)

=(x+4)(x-3)

8: (x+1)(x+3)(x+5)(x+7)+15

\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)

\(=\left(x^2+8x+7\right)^2+8\left(x^2+8x+7\right)+15\)

\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)

\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)