-7x(2x²- 4x - 5) - (x - 5)(-2x + 3) + (3x - 2)(x+4) - 4x² (x - 3)

=-14x³+28x²+35x+2x²-3x-10x+15+3x²+12x-2x-8-4x³+12x²

=-18x³+45x²+32x+7

(x - 6)(3x - 1) - 2x²(x - 2) + x(x - 1)(2x + 3) - 5x(x² - 4x + 1) 

= (3x² - 19x + 6) - (2x³ - 4x²) + (x² - x)(2x + 3) - (5x³ - 20x² + 5x) 

= 3x² - 19x + 6 - 2x³ + 4x² + 2x³ + 3x² - 2x² - 3x - 5x³ + 20x² + 5x

= -7x³ + 28x²+ 17x + 6 

dài lắm nên mình làm tắt

1) (x - 5)^2 + (x + 3)^2 = 2(x - 4)(x + 4) - 5x + 7

<=> x^2 - 10x + 25 + x^2 + 6x + 9 = 2x^2 + 8x - 8x - 32 - 5x + 7

<=> 2x^2 - 4x + 34 = 2x^2 - 5x - 25

<=> -4x + 34 = -5x - 25

<=> x + 34 = -25

<=> x = -25 - 34

<=> x = - 59

2) (x + 3)(x - 2) - 2(x + 1)^2 = (x - 3)^2 - 2x^2 + 4x

<=> x^2 - 2x + 3x - 6 - 2x^2 - 4x - 2 = x^2 - 6x + 9 - 2x^2 + 4x

<=> -x^2 - 3x - 8 = -x^2 - 2x + 9

<=> -3x - 8 = -2x + 9

<=> -x - 8 = 9

<=> -x = 9 + 8

<=> x = -17

3) (x + 1)^3 - (x + 2)(x - 4) = (x - 2)(x^2 + 2x + 4) + 2x^2

<=> x^3 + 2x^3 + x + x^2 + 2x + 1 - x^2 + 4x - 2x + 8 = x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 + 2x^2

<=> 2x^2 + 5x + 9 = 2x^2 - 8

<=> 5x + 9 = -8

<=> 5x = -8 - 9

<=> 5x = -17

<=> x = -17/5

4) (x - 2)^3 + (x - 5)(x + 5) = x(x^2 - 5x) - 7x + 3

<=> x^3 - 4x^2 + 4x - 2x^2 + 8x - 8 + x^2 - 5^2 = x^3 - 5x^2 - 7x + 3

<=> 12x - 33 = -7x + 3

<=> 19x - 33 = 3

<=> 19x = 3 + 33

<=> 19x = 36

<=> x = 36/19

5) (x + 4)(x^2 - 4x + 16) - x(x - 4)^2 = 8(x - 3)(x + 3)

<=> x^3 - 4x^2 + 16x + 4x^2 - 16x + 64 - x^3 + 8x^2 - 16x = 8x^2 - 72

<=> -16x + 64 = -72

<=> -16x = -72 - 64

<=> -16x = -136

<=> x = 136/16 = 17/2

6) 4(x - 1)(x + 2) - 5(x + 7) = (2x + 3)^2 - 5x + 3

<=> 4x^2 + 8x - 4x - 8 - 5x - 35 = 4x^2 + 12x + 9 - 5x + 3

<=> -x - 43 = 7x + 12

<=> -8x - 43 = 12

<=> -8x = 12 + 43

<=> -8x = 55

<=> x = -55/8

7) (x - 1)(x^2 + x + 1) + 3(x - 2)^2 = x(x^2 + 3x - 1)

<=> x^3 + x^2 + x - x^2 - x - 1 + 3x^2 - 12x + 12 = x^3 + 3x^2 - x

<=> 3x^2 - 12x + 11 = 3x^2 - x

<=> -12x + 11 = -x

<=> 11 = -x + 12x

<=> 11 = 11x

<=> x = 1

8) (x + 5)(x - 5) - (x + 3)(x^2 - 3x + 9) = 5 - x(x^2 - x - 2)

<=> x^2 - 25 - x^3 + 3x^2 - 9 - 3x^2 + 9x - 27 = 5 - x^3 + x^2 + 2x

<=> -52 - x^3 = 5 - x^3 + 2x

<=> -52 = 5x + 2x

<=> -5x - 2x = 52

<=> -7x = 52

<=> x = -52/7

9) (x + 2)^2 - 2(x + 3)(x - 4) = 5 - x(x - 3)

<=> x^2 + 4x + 4 - 2x^2 + 8x - 6x + 24 = 5 - x^3 + 3x

<=> 6x + 28 = 5 + 3x

<=> 6x + 28 - 3x = 5

<=> 3x + 28 = 5

<=> 3x = 5 - 28

<=> 3x = -23

<=> x = -23/3

10)  (x + 7)(x - 7) - (x + 2)^2 = 5(x - 2) + (x - 7)

<=> x^2 - 49 - x^2 - 4x - 4 = 5x - 10 + x - 7

<=> -53 - 4x = 6x - 17

<=> -4x = 6x + 36

<=> -4x - 6x = 36

<=> -10x = 36

<=> x = -36/10 = -18/5

(-3x + 4)(x - 2) - x(x² - 2)(-4x + 1) + (2x - 5)(x² - 4x)

= -3x² + 10x - 8 - x(-4x³ + x² + 8x - 2) + 2x³ - 13x² + 20x

= 2x³ - 16x² + 30x - 8 + 4x⁴ - x³ - 8x² + 2x

= 4x⁴ + x³ - 24x² + 28x - 8

5x² (x - 7) - 4x(x - 2)(x + 3) - (x - 5)(x + 6) + (2x-1)(x + 5)

=5x³-35x²-4x(x²+3x-2x-6)-(x²+6x-5x-30)+2x²+10x-x-5

=5x³-35x²-4x³-12x²+8x²+24x-x²-6x+5x+30+2x²+9x-5

=x³+32x²+32x+25

a) (2x - 1)(3x + 5) - 2(-4x + 1)² = 6x² + 10x - 3x - 5 - 2(16x² - 8x + 1) = 6x² - 3x - 5 - 32x² + 16x - 2 = -26x² + 13x - 7

b) \(\frac{x^2-16}{4x-x^2}=\frac{\left(x-4\right)\left(x+4\right)}{-x\left(x-4\right)}=-\frac{x+4}{x}\)

c) \(\frac{2x-9}{x^2-5x+6}+\frac{2x+1}{x-3}+\frac{x+3}{2-x}\)

= \(\frac{2x-9}{x^2-2x-3x+6}+\frac{\left(2x+1\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}-\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}\)

= \(\frac{2x-9+2x^2-3x-2-x^2+9}{\left(x-3\right)\left(x-2\right)}\)

= \(\frac{x^2-x-2}{\left(x-3\right)\left(x-2\right)}\)

= \(\frac{x^2-2x+x-2}{\left(x-3\right)\left(x-2\right)}\)

= \(\frac{\left(x+1\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}=\frac{x+1}{x-3}\)

d) (x - 1)³ - (x + 1)³ + 6(x + 1)(x - 1)

= (x - 1 - x - 1)[(x - 1)² + (x - 1)(x + 1) + (x + 1)²] + 6(x² - 1)

= -2(x² - 2x + 1  + x² - 1 + x² + 2x + 1) + 6x² - 6

= -2(3x² + 1) + 6x² - 6

= -6x² - 2 + 6x²  - 6

= -8

e) (2x + 7)² - (4x + 14)(2x - 8) + (8 - 2x)²

= (2x + 7)² - 2(2x + 7)(2x - 8) + (2x - 8)²

= (2x + 7 - 2x + 8)²

= 15² = 225

Bài1: Phân tích các đa thức sau thành nhân tử

a)36-4x²+4xy-y²

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

\(=6^2-\left(2x-y\right)^2\)

\(=\left(6+2x-y\right)\left(6-2x+y\right)\)

b)2x⁴+3x²-5

\(=2x^4-2x^2+5x^2-5\)

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

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

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

B1:a)\(36-4x^2+4xy-y^2=36-\left(4x^2-4xy+y^2\right)=6^2-\left(2x-y\right)^2\)

\(=\left(6-2x+y\right)\left(6+2x-y\right)\)

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

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

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

(5x - 2)(x + 1) - 3x(x² - x - 3) - 2x(x - 5)(x + 4) + 5x(x² - 7)

= 5x² + 3x - 2 - 3x³ + 3x² + 9x - 2x(x² - x - 20) + 5x³ - 35x

= 2x³ + 8x² - 23x - 2 - 2x³ + 2x² + 40x = 10x² + 17x - 2

4x(x²-2x+3)-3x(x+1)(x-2)+(2x-5)(x-7)-4x(x²-x+1)

=4x³-8x²+12x-3x(x²-2x+x-2)+2x²-14x-5x+35-4x³+4x²-4x

=4x³-8x²+12x-3x³+6x²-3x²+6x+2x²-14x-5x+35-4x³+4x²-4x

=-3x³+x²-5x+35

#H