a) \(A=5x\left(4x^2-2x+1\right)-2x\left(10x^2-5x-2\right)\)

\(A=20x^3-10x^2+5x-20x^3+10x^2+4x\)

\(A=9x\)

Thay x = 15 vào, ta có: 

\(A=9.15=135\)

b) \(B=5x\left(x-4y\right)-4y\left(y-5x\right)\)

\(B=5x^2-20xy-4y^2+20xy\)

\(B=5x^2-4y\)

Thay \(x=-\frac{1}{5};y=-\frac{1}{2}\) vào, ta có: 

\(B=5.\left(-\frac{1}{5}\right)^2-4.\left(-\frac{1}{2}\right)=\frac{11}{5}\)

c) \(C=6xy\left(xy-y^2\right)-8x^2\left(x-y^2\right)-5y^2\left(x^2-xy\right)\)

\(C=6x^2y^2-6xy^3-8x^3+8x^2y^2-5x^2y^2+5xy^3\)

\(C=9x^2y^2-xy^3-8x^3\)

Thay \(x=\frac{1}{2};y=2\) vào, ta có:

\(C=9.\left(\frac{1}{2}\right)^2.2^2-\frac{1}{2}.2^3-8.\left(\frac{1}{2}\right)^3=4\)

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

\(D=6x^2-3x+10x-5+12x^2+8x-3x-2\)

\(D=18x^2+12x-7\)

Ta có: \(\left|2\right|=\orbr{\begin{cases}x=-2\\x=2\end{cases}}\)

+) Với x = -2

\(D=18.\left(-2\right)^2+12.\left(-2\right)-7=41\)

+) Với x = 2

\(D=18.2^2+12.2-7=89\)

a) Xem lại đề

b) x³ - 4x²y + 4xy² - 9x

= x(x² - 4xy + 4y² - 9)

= x[(x² - 4xy + 4y² - 3²]

= x[(x - 2y)² - 3²]

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

c) x³ - y³ + x - y

= (x³ - y³) + (x - y)

= (x - y)(x² + xy + y²) + (x - y)

= (x - y)(x² + xy + y² + 1)

d) 4x² - 4xy + 2x - y + y²

= (4x² - 4xy + y²) + (2x - y)

= (2x - y)² + (2x - y)

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

e) 9x² - 3x + 2y - 4y²

= (9x² - 4y²) - (3x - 2y)

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

= (3x - 2y)(3x + 2y - 1)

f) 3x² - 6xy + 3y² - 5x + 5y

= (3x² - 6xy + 3y²) - (5x - 5y)

= 3(x² - 2xy + y²) - 5(x - y)

= 3(x - y)² - 5(x - y)

= (x - y)[(3(x - y) - 5]

= (x - y)(3x - 3y - 5)

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

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

= (2 - x)(x + y)

2/ 5x² - 5xy -10x + 10y

= 5x(x - y) - 10(x - y)

= (5x - 10(x - y)

3/ 4x² + 8xy - 3x - 6y

= 4x(x + 2y) - 3(x + 2y)

= (4x - 3)(x + 2y)

1) 2x + 2y - x(x + y) 

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

= (2 - x)(x + y)

2) 5x² - 5xy - 10x + 10y 

= 5x(x - y) - 10(x - y)

= (5x - 10)(x - y)

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

3) 4x² + 8xy - 3x - 6y  

= 4x(x + 2y) - 3(x + 2y)

= (4x - 3)(x + 2y)

4) 2x² + 2y² - x²z + z - y²z - 2 

= 2(x² + y² - z(x² + y²) - (2 - z)

= (2 - z)(x² + y²) - (2 - z)

= (2 - z)(x² + y²)

5) x² + xy - 5x - 5y

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

= (x - 5)(x + y)

6) x(2x - 7) - 4x + 14 

= x(2x - 7) - 2(2x - 7) 

= (x - 2)(2x - 7)

7)x² - 3x + xy - 3y  

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

= (x - 3)(x + y)

5/ x² + xy - 5x - 5y 

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

= (x - 5)(x + y)

6/ x(2x - 7) - 4x + 14

= 2x² - 7x - 4x + 14

= (2x² - 4x) - (7x - 14)

= 2x(x - 2) -7(x - 2)

= (2x - 7)(x - 2)

7/ x² - 3x + xy - 3y

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

= (x + y)(x - 3) 

a: 2x^2y-50xy=2xy(x-25)

b: 5x^2-10x=5x(x-2)

c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)

d: \(x^2-xy+x=x\left(x-y+1\right)\)

e: x(x-y)-2(y-x)

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

=(x-y)(x+2)

f: 4x^2-4xy-8y^2

=4(x^2-xy-2y^2)

=4(x^2-2xy+xy-2y^2)

=4[x(x-2y)+y(x-2y)]

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

f1: x^2ỹ-y^2+y

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

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

B=[(x - 2)(x - 5)](x²– 7x - 10) 
= (x²- 7x + 10)(x² - 7x - 10)
= (x² - 7x)²- 10²
= (x² - 7x)² - 100

=>(x²-7x)²\(\ge\) 100

GTNN = -100 \(\Rightarrow\) x² - 7x = 0 \(\Leftrightarrow\) x(x-7) = 0 \(\Leftrightarrow\) x = 0 hoặc x = 7

B = x² - 4xy + 5y² + 10x - 22y + 28 
= x² - 4xy + 4y²+ y²+ 10(x-2y) + 28 
= (x - 2y)²+ 10(x-2y) + 25 + y²- 2y+ 1 + 2 
= (x-2y + 5)² + (y-1)² + 2\(\ge\) 2 
GTNN B = 2, khi y=1, x=-3