\(\left(10^2+8^2+...+2^2\right)-\left(9^2+7^2+...+1^2\right)\)

\(=\left(10^2-9^2\right)+\left(8^2-7^2\right)+...+\left(2^2-1^2\right)\)

\(=\left(10-9\right)\left(10+9\right)+\left(8-7\right)\left(8+7\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=19+15+...+3\)

\(=\frac{\left(3+19\right)x\left[\left(19-3\right):4+1\right]}{2}\)

\(=\frac{21.5}{2}=\frac{105}{2}=52,5\)

a) x^3-2x^2+x

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

x(x-1)^2

b) x^2-2x-15

= (x^2-2x+1)-16

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

= ( x-5)(x+3)

d) 5(x-y)-y(x-y)

=(x-y)(5-y)

e) 27x^2(y-1)-9x^3(1-y)

= 27x^2(y-1)+9x^3(y-1)

= (y-1)(27x^2+9x^3)

= 9x^2(y-1)(3+x)

f) 36-12x+x^2

= x^2- 6.2x+36

= ( x - 6)^2

g) 125^3+27y^3

125^3+ ( 9y)^3

= 125^3+ 3.125^2.9y+3.125.(9y)2+ (9y)3

i) xy+xz+3y+3z

= x( x+y) + 3(y+z)

= (y+z)(x+3)

a/ \(x^3-2x^2+x\)

= \(x\left(x^2-2x+1\right)\)

= \(x\left(x-1\right)^2\)

b/ \(x^2-2x-15\)

= \(x^2-2x+1-16\)

= \(\left(x-1\right)^2-4^2\)

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

= \(\left(x-5\right)\left(x+3\right)\)

c/ \(x^2-2x-y^2+1\)

= \(\left(x-1\right)^2-y^2\)

= \(\left(x-y-1\right)\left(x+y-1\right)\)

d/ \(5\left(x-y\right)-y\left(x-y\right)\)

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

e/ \(27x^2\left(y-1\right)-9x^3\left(1-y\right)\)

= \(27x^2\left(y-1\right)+9x^3\left(y-1\right)\)

= \(\left(y-1\right)\left(27x^2+9x^3\right)\)

f/ \(36-12x+x^2\)

= \(x^2-12x+6^2\)

= \(\left(x-6\right)^2\)

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

\(=x^2-10x+25+4+4x+x^2\)

\(=2x^2-6x+29\)

Đề này là phân tích đa thức thành nhân tử nha bạn

a/ \(x^2+6x-4y^2+9\)

= \(x^2+6x+9-4y^2\)

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

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

b/ \(x^2-2xy+2zt+y^2-z^2-t^2\)

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

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

= \(\left(x-y-z+t\right)\left(x-y+z-t\right)\)

c/ \(2x^2+4x+2-2y^2\)

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

= \(2\left(x^2-y^2+2x+1\right)\)

= \(2\left[\left(x+1\right)^2-y^2\right]\)

= \(2\left(x+1-y\right)\left(x+1+y\right)\)

d/ \(x^2-2x-8\)

= \(x^2-2x+1-9\)

= \(\left(x-1\right)^2-3^2\)

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

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

a, =x²(x-3)-4(x-3)=(x²-4)(x-3)=(x-2)(x+2)(x-3)

b, =x³(x+1)+(x+1)=(x³+1)(x+1)

c, =x³(x-1)-(x-1)(x+1)=(x³-x-1)(x-1)

d, =(2x+1+x-1)(2x+1-x+1)=3x(x+2)

e, =x⁴+4x²+4-9=(x²+2)²-3²=(x²+2+3)(x²+2-3)=(x²+5)(x²-1)

a)  (x-3)(x-2)(x+2)

b)  (x+1)²(x²-x+1)

c)  (x-1)(x³+x+1)

d)  3x(x+2)

e)  (x²+5)(x+1)(x-1)