a. Để tính \( a + b \), \( b + c \), \( a - c \), và \( b - a \), chúng ta chỉ cần thêm các đa thức lại với nhau:

\( a + b = (2x^4 - x + 3x^2 - 6) + (-x^4 + 2 - 3x^2 - 5x) \) \
\( = 2x^4 - x + 3x^2 - 6 - x^4 + 2 - 3x^2 - 5x \) \
\( = x^4 - 6x - 6 \)

\( b + c = (-x^4 + 2 - 3x^2 - 5x) + (-2x^3 + 1 - 3x + x^2) \) \
\( = -x^4 + 2 - 3x^2 - 5x - 2x^3 + 1 - 3x + x^2 \) \
\( = -x^4 - 2x^3 - 2x^2 - 8x + 3 \)

\( a - c = (2x^4 - x + 3x^2 - 6) - (-2x^3 + 1 - 3x + x^2) \) \
\( = 2x^4 - x + 3x^2 - 6 + 2x^3 - 1 + 3x - x^2 \) \
\( = 2x^4 + 2x^3 + 2x^2 + 2x - 7 \)

\( b - a = (-x^4 + 2 - 3x^2 - 5x) - (2x^4 - x + 3x^2 - 6) \) \
\( = -x^4 + 2 - 3x^2 - 5x - 2x^4 + x - 3x^2 + 6 \) \
\( = -3x^4 - 7x + 8 \)

b. Để tính \( m = a - b + c \):

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

c. Để tính \( n = b - c - a \):

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

a. Để tính a+b𝑎+𝑏, b+c𝑏+𝑐, a−c𝑎−𝑐, và b−a𝑏−𝑎, chúng ta chỉ cần thêm các đa thức lại với nhau:

a+b=(2x4−x+3x2−6)+(−x4+2−3x2−5x)𝑎+𝑏=(2𝑥4−𝑥+3𝑥2−6)+(−𝑥4+2−3𝑥2−5𝑥) \
=2x4−x+3x2−6−x4+2−3x2−5x=2𝑥4−𝑥+3𝑥2−6−𝑥4+2−3𝑥2−5𝑥 \
=x4−6x−6=𝑥4−6𝑥−6

b+c=(−x4+2−3x2−5x)+(−2x3+1−3x+x2)𝑏+𝑐=(−𝑥4+2−3𝑥2−5𝑥)+(−2𝑥3+1−3𝑥+𝑥2) \
=−x4+2−3x2−5x−2x3+1−3x+x2=−𝑥4+2−3𝑥2−5𝑥−2𝑥3+1−3𝑥+𝑥2 \
=−x4−2x3−2x2−8x+3=−𝑥4−2𝑥3−2𝑥2−8𝑥+3

a−c=(2x4−x+3x2−6)−(−2x3+1−3x+x2)𝑎−𝑐=(2𝑥4−𝑥+3𝑥2−6)−(−2𝑥3+1−3𝑥+𝑥2) \
=2x4−x+3x2−6+2x3−1+3x−x2=2𝑥4−𝑥+3𝑥2−6+2𝑥3−1+3𝑥−𝑥2 \
=2x4+2x3+2x2+2x−7=2𝑥4+2𝑥3+2𝑥2+2𝑥−7

b−a=(−x4+2−3x2−5x)−(2x4−x+3x2−6)𝑏−𝑎=(−𝑥4+2−3𝑥2−5𝑥)−(2𝑥4−𝑥+3𝑥2−6) \
=−x4+2−3x2−5x−2x4+x−3x2+6=−𝑥4+2−3𝑥2−5𝑥−2𝑥4+𝑥−3𝑥2+6 \
=−3x4−7x+8=−3𝑥4−7𝑥+8

b. Để tính m=a−b+c𝑚=𝑎−𝑏+𝑐:

m=(2x4−x+3x2−6)−(−x4+2−3x2−5x)+(−2x3+1−3x+x2)𝑚=(2𝑥4−𝑥+3𝑥2−6)−(−𝑥4+2−3𝑥2−5𝑥)+(−2𝑥3+1−3𝑥+𝑥2) \
=2x4−x+3x2−6+x4−2+3x2+5x−2x3+1−3x+x2=2𝑥4−𝑥+3𝑥2−6+𝑥4−2+3𝑥2+5𝑥−2𝑥3+1−3𝑥+𝑥2 \
=3x4−2x3+7x2−4x−7=3𝑥4−2𝑥3+7𝑥2−4𝑥−7

c. Để tính n=b−c−a𝑛=𝑏−𝑐−𝑎:

n=(−x4+2−3x2−5x)−(−2x3+1−3x+x2)−(2x4−x+3x2−6)𝑛=(−𝑥4+2−3𝑥2−5𝑥)−(−2𝑥3+1−3𝑥+𝑥2)−(2𝑥4−𝑥+3𝑥2−6) \
=−x4+2−3x2−5x+2x3−1+3x−x2−2x4+x−3x2+6=−𝑥4+2−3𝑥2−5𝑥+2𝑥3−1+3𝑥−𝑥2−2𝑥4+𝑥−3𝑥2+6 \
=−3x4+2x3+5x2−7x+7=−3𝑥4+2𝑥3+5𝑥2−7𝑥+7
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