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

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

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

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

b, Ta có : \(H\left(x\right)=F\left(x\right)-G\left(x\right)=2x^3-4x^2-x-10-2x^3+4x^2+4x-2\)

\(\Leftrightarrow3x-12=0\Leftrightarrow x=4\)

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

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

\(=2x^2+2\)

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

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

\(=4x+5\)

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

\(=x^2-6x+9+3x^2+6x+3\)

\(=4x^2+12\)

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

\(=9x^2-4-9x^2-6x-1\)

\(=-6x-5\)

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

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

\(=-x-14\)

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

\(=2x^2-5x+6x-15-2-4x-2x^2\)

\(=-3x-17\)

g) \(\left(4x-1\right)\left(4x+1\right)-4\left(1-2x\right)^2\)

\(=16x^2-1-4+16x-16x^2\)

\(=16x-5\)

#Học tốt!

a: \(=\dfrac{x^4-6x^3+12x^2-14x+3}{x^2-4x+1}\)

\(=\dfrac{x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3}{x^2-4x+1}\)

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

b: \(=\dfrac{x^5-3x^4+5x^3-x^2+3x-5}{x^2-3x+5}=x^2-1\)

c: \(=\dfrac{2x^4-5x^3+2x^2+2x-1}{x^2-x-1}\)

\(=\dfrac{2x^4-2x^3-2x^2-3x^3+3x^2+3x+x^2-x-1}{x^2-x-1}\)

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

a) Sắp xếp các hạng tử của mỗi đa thức theo lũy thừa tăng của biến.

Thu gọn: P(x) = 3x² - 5 + x⁴ - 3x³ - x⁶ - 2x² - x³

= x² - 5 + x⁴ - 4x³ - x⁶

Sắp xếp: P(x) = -5 + x² - 4x³ + x⁴ - x⁶

Thu gọn: Q(x) = x³ + 2x⁵ - x⁴ + x² - 2x³ + x - 1= -x³ +2x⁵ - x⁴ + x² + x - 1

Sắp xếp: Q(x) = -1 + x + x² - x³ - x⁴ + 2x⁵

b) Ta có:

.

a) Sắp xếp các hạng tử của mỗi đa thức theo lũy thừa tăng của biến.

Thu gọn: P(x) = 3x² - 5 + x⁴ - 3x³ - x⁶ - 2x² - x³

= x² - 5 + x⁴ - 4x³ - x⁶

Sắp xếp: P(x) = -5 + x² - 4x³ + x⁴ - x⁶

Thu gọn: Q(x) = x³ + 2x⁵ - x⁴ + x² - 2x³ + x - 1= -x³ +2x⁵ - x⁴ + x² + x - 1

Sắp xếp: Q(x) = -1 + x + x² - x³ - x⁴ + 2x⁵

b) Ta có:

a)\(9x^2+30x+25+9x^2-30x+25-\left(9x^2-2^2\right)\)

=\(9x^2+54\)=\(9\left(x^2+6\right)\)

b)\(2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)

=\(8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)

=\(x^3-16x^2+25x\)

c)\(\left(x+y-z\right)^2-2\left(x+y-z\right)\left(x+y\right)+\left(x+y\right)^2\)

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

\(a,\left(3x+5\right)^2+\left(3x-5\right)^2-\left(3x+2\right)\left(3x-2\right)=9x^2+30x+25+9x^2-30x+25-9x^2+4=9x^2+54\)
\(b,BT=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x=x^3-16x^2+25x\)
\(c,BT=\left(x+y-z\right)^2-2\left(x+y-z\right)\left(x+y\right)+\left(x+y\right)^2=\left(x+y-z-x-y\right)^2=z^2\)

Lời giải:

a)

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

\(=3\) không phụ thuộc vào biến (đpcm)

b)

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

\(=4x-24-2x^2-3x^3+5x^2-4x+3x^3-3x^2\)

\(=(4x-4x)-24+(-2x^2+5x^2-3x^2)+(-3x^3+3x^3)\)

\(=-24\) không phụ thuộc vào biến.

c)

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

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

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

\(=3\) không phụ thuộc vào biến (đpcm)

a)

\(A=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)

\(=x^3-3x^2+9x+3x^2-9x+27-54-x^3\)

\(=-27\)

or

\(A=x^3+27-54-x^3=-27\)

b)

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

\(=8x^3+y^3-8x^3+y^3=2y^3\)

c)

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

\(=\left(2x+1+3x-1\right)^2=\left(5x\right)^2=25x^2\)

d)

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

\(=x^3-8-\left(x-1\right)^3+3\left(x-1\right)\left(x+1\right)\)

\(=6x^2-3x-10\)