a) (7x - 8)(7x + 8) - 10(2x + 3)² + 5x(3x - 2)² - 4x(x - 5)²

= 49x² - 64 - 10(4x² + 12x + 9) + 5x(9x² - 12x + 4)  - 4x(x²  - 10x + 25)

= 49x² - 64 - 40x² - 120x - 90 + 45x³ - 60x² + 20x - 4x³ + 40x - 100x

= 41x³ - 51x² - 160x - 154

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

= x⁴ - 9 - 5x2(x² + 2x + 1) - x⁴ + 5x³ - 6x² + 4x(x² + 4x + 4)

= 5x³ - 6x² - 5x⁴ - 10x³ - 5x² + 4x³ + 16x² + 16x - 9

= -5x⁴ - x³ + 5x² + 16x - 9

Trả lời:

a , ( 7x - 8 ) ( 7x + 8 ) - 10 ( 2x + 3 )² + 5x ( 3x - 2 )² - 4x ( x - 5 )²

= 49x² - 64 - 10 ( 4x² + 12x + 9 ) + 5x ( 9x² - 12x + 4 ) - 4x ( x² - 10x + 25 )

= 49x² - 64 - 40x² + 120x - 90 + 45x³ - 60x² + 20x - 4x³ + 40x² - 100x

= 41x³ - 11x² + 40x - 154

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

= x⁴ - 9 - 5x² ( x² + 2x + 1 ) - ( x⁴ - 2x³ - 3x³ + 6x² ) + 4x ( x² + 4x + 4 )

= x⁴ - 9 - 5x⁴ - 10x³ - 5x² - x⁴ + 2x³ + 3x³ - 6x² + 4x³ + 16x² + 16x

= - 5x⁴ - x³ + 5x² + 16x - 9

\(a,\left(6x+1\right)\left(x+2\right)-2x\left(3x-5\right)\)

\(=6x^2+12x+x+2-6x^2+10x\)

\(=23x+2\)

a) (6x + 1)(x + 2) - 2x(3x - 5)

= 6x² + 12x + x + 2 - 6x² + 10x

= (6x² - 6x²) + (12x + x + 10x) + 2

= 23x + 2

b) (2x - 1)² - (2x - 3)(2x + 3)

= 4x² - 4x + 1 - 4x² + 9

= (4x² - 4x²) - 4x + (1 + 9)

= -4x + 10

c) (2x - 3)³  - (3x  + 1)(5 - 4x) - 16x²

= 8x³ - 36x² + 54x - 15x + 12x² - 5 + 4x - 16x²

= 8x³ - (36x² - 12x² + 16x²) + (54x - 15x + 4x) - 5

= 8x³ - 40x² + 43x - 5

d) (3x + 2) - (x - 5) - x(3x - 13)

= 3x  + 2 - x + 5 - 3x² + 13x

= (3x - x + 13x) + (2 + 5) - 3x²

= 15x + 7 - 3x²

Bài 2:

a) \(x^2+y^2-9-2xy\)

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

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

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

b) \(4x^2-5x-9\)

\(=4x^2+4x-9x-9\)

\(=4x\left(x+1\right)-9\left(x+1\right)\)

\(=\left(x+1\right)\left(4x-9\right)\)

\(\left(2x-3\right)^2-\left(4x-1\right)\left(x+2\right)=4x^2-12x+9-4x^2-7x+2=-19x+11\)

\(\left(3x+2\right)\left(3x-2\right)-\left(3x-1\right)^2=9x^2-4-9x^2+6x-1=6x-5\)

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

\(4x^2-5x-9=\left(4x-9\right)\left(x+1\right)\)

\(\left(x-3\right)^2-\left(x-1\right)\left(x-2\right)=5\Leftrightarrow x^2-6x+9-x^2+3x-2=5\)

\(\Leftrightarrow-3x=-2\Leftrightarrow x=x=\frac{2}{3}\)

\(3x^2+5x-8=0\Leftrightarrow\left(x-1\right)\left(3x+8\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-\frac{8}{3}\end{cases}}\)

Bài2: phân tích đa thức thành nhân tử 

\(a,x^2-y^2-2x+2y\)

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

\(b,x^3-5x^2+x-5\)

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

\(=\left(x+x-5\right)\left(x-x-5\right)\)

  \(c,x^2-2xy+y^2-9\)

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

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

chúc bạn học tốt !

a) A = (3x - 5)(2x + 11) - (2x + 3)(3x + 7)

A = 6x^2 + 33x - 10x - 55 - 6x^2 - 23x - 21

A = -76

b) B = 4x(3x - 2) - 3x(4x + 1)

B = 12x^2 - 8x - 12x^2 - 3x

B = -11x

c) C = (x + 3)(x - 2) - (x - 1)^2

C = x^2 + x - 6 - x^2 + 2x - 1

C = 3x - 7

a) \(\left(2x-1\right)^2-\left(x+2\right)^2-3x^2+5x\)

\(=4x^2-4x+1-\left(x^2+4x+4\right)-3x^2+5x\)

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

b) \(\left(x+2\right)\left(x-1\right)+2\left(3x-2\right)^2+4x-19x^2\)

\(=x^2+2x-x-2+2\left(9x^2-12x+4\right)+4x-19x^2\)

\(=x^2+2x-x-2+18x^2-24x+8+4x-19x^2\)

\(=-19x+6\)

c) \(2\left(3-x\right)\left(x-2\right)-\left(3x+1\right)^2+5x-11x^2\)

\(=6-2x\left(x-2\right)-\left(9x^2+6x+1\right)+5x-11x^2\)

\(=6-2x^3+4x-9x^2-6x-1+5x-11x^2\)

\(=-2x^3-20x^2+3x+5\)

(4x-1)(3x+1)-5x²(x-3)-(x-4)(x-3)-7(x³-2x²+x-1)

=12x²+4x-3x-1-5x³+15x²-x²+3x+4x-12-7x³+14x²-7x+7

=-12x³40x²+x-6

#H

(4x-1)(3x+1)-5x²(x-3)-(x-4)(x-3)-7(x³-2x²+x-1)

= 12x²+4x-3x-1-5x³+15x²-x²-3x-4x+12-7x³+14x²-7x-1

=-12x³+40x²-13x+10