a) (-2x^4 + 4x^3 + 6x^2 - 10x) + (x^4 + 2x^3 - 15x) =

b) (x^2 - 4x + 12) + (2x^3 - 4x + 20) =

c) (x^3 + 4x^2 - 6) + (2x^4 - x^5 + 3x^3) =

d) (6x^5 - 2x^7 + 3x^3 - 5x + 2x^4) + (6x^5 - 3x^7 - 2x^6 + 4x^2 - 7) =

e) (3x^4 + 7x^3 + 3x^2 - 2x) - (5x^4 + 4x^3 - 6x + 2) =

f) (x^2 + 14x - 6) - (3x^3 - 3x^2 + 10x + 5) =

g) (6x - 5x^4 + 4x^5 - 2x^7) - (-7x^5 + 5x - 2x^4 + 3x^2 - 5) =

h) (-3ab + 5a^2b + 4ab^2 - 6) - (4a^2b + 3ab^2 - 5 + 2ab) =

i) (x^2 + 30x + 225) - (4x^2 + 12x + 9) =

j) (x^3 + 3x^2 + 3x + 1) + (8x^3 + 12x^2 - 6x - 18) =

Q: a) (-2x^4 + 4x^3 + 6x^2 - 10x) + (x^4 + 2x^3 - 15x) = b) (x^2 - 4x + 12) + (2x^3 - 4x + 20) = c) (x^3 + 4x^2 - 6) + (2x^4 - x^5 + 3x^3) = d) (6x^5 - 2x^7 + 3x^3 - 5x + 2x^4) + (6x^5 - 3x^7 - 2x^6 + 4x^2 - 7) = e) (3x^4 + 7x^3 + 3x^2 - 2x) - (5x^4 + 4x^3 - 6x + 2) = f) (x^2 + 14x - 6) - (3x^3 - 3x^2 + 10x + 5) = g) (6x - 5x^4 + 4x^5 - 2x^7) - (-7x^5 + 5x - 2x^4 + 3x^2 - 5) = h) (-3ab + 5a^2b + 4ab^2 - 6) - (4a^2b + 3ab^2 - 5 + 2ab) = i) (x^2 + 30x + 225) - (4x^2 + 12x + 9) = j) (x^3 + 3x^2 + 3x + 1) + (8x^3 + 12x^2 - 6x - 18) =

Let's solve each expression: a) $(-2x^4 + 4x^3 + 6x^2 - 10x) + (x^4 + 2x^3 - 15x)$ Combine like terms: \[ (-2x^4 + x^4) + (4x^3 + 2x^3) + 6x^2 + (-10x - 15x) \] \[ = -x^4 + 6x^3 + 6x^2 - 25x \] b) $(x^2 - 4x + 12) + (2x^3 - 4x + 20)$ Combine like terms: \[ 2x^3 + x^2 + (-4x - 4x) + (12 + 20) \] \[ = 2x^3 + x^2 - 8x + 32 \] c) $(x^3 + 4x^2 - 6) + (2x^4 - x^5 + 3x^3)$ Combine like terms: \[ (-x^5) + 2x^4 + (x^3 + 3x^3) + 4x^2 - 6 \] \[ = -x^5 + 2x^4 + 4x^3 + 4x^2 - 6 \] d) $(6x^5 - 2x^7 + 3x^3 - 5x + 2x^4) + (6x^5 - 3x^7 - 2x^6 + 4x^2 - 7)$ Combine like terms: \[ (-2x^7 - 3x^7) + (6x^5 + 6x^5) + 2x^4 + 3x^3 + 4x^2 - 5x - 7 \] \[ = -5x^7 + 12x^5 + 2x^4 + 3x^3 + 4x^2 - 5x - 7 \] e) $(3x^4 + 7x^3 + 3x^2 - 2x) - (5x^4 + 4x^3 - 6x + 2)$ Combine like terms: \[ (3x^4 - 5x^4) + (7x^3 - 4x^3) + 3x^2 + (-2x + 6x) - 2 \] \[ = -2x^4 + 3x^3 + 3x^2 + 4x - 2 \] f) $(x^2 + 14x - 6) - (3x^3 - 3x^2 + 10x + 5)$ Combine like terms: \[ -3x^3 + (x^2 + 3x^2) + (14x - 10x) + (-6 - 5) \] \[ = -3x^3 + 4x^2 + 4x - 11 \] g) $(6x - 5x^4 + 4x^5 - 2x^7) - (-7x^5 + 5x - 2x^4 + 3x^2 - 5)$ Combine like terms: \[ (-2x^7) + (4x^5 + 7x^5) + (-5x^4 + 2x^4) + (6x - 5x) - 3x^2 + 5 \] \[ = -2x^7 + 11x^5 - 3x^4 + x - 3x^2 + 5 \] h) $(-3ab + 5a^2b + 4ab^2 - 6) - (4a^2b + 3ab^2 - 5 + 2ab)$ Combine like terms: \[ (-3ab - 2ab) + (5a^2b - 4a^2b) + (4ab^2 - 3ab^2) + (-6 + 5) \] \[ = -5ab + a^2b + ab^2 - 1 \] i) $(x^2 + 30x + 225) - (4x^2 + 12x + 9)$ Combine like terms: \[ (x^2 - 4x^2) + (30x - 12x) + (225 - 9) \] \[ = -3x^2 + 18x + 216 \] j) $(x^3 + x^2 + 3x + 1) + (8x^3 + 12x^2 - 6x - 18)$ Combine like terms: \[ (x^3 + 8x^3) + (x^2 + 12x^2) + (3x - 6x) + (1 - 18) \] \[ = 9x^3 + 13x^2 - 3x - 17 \]

Question

a) (-2x^4 + 4x^3 + 6x^2 - 10x) + (x^4 + 2x^3 - 15x) =

b) (x^2 - 4x + 12) + (2x^3 - 4x + 20) =

c) (x^3 + 4x^2 - 6) + (2x^4 - x^5 + 3x^3) =

d) (6x^5 - 2x^7 + 3x^3 - 5x + 2x^4) + (6x^5 - 3x^7 - 2x^6 + 4x^2 - 7) =

e) (3x^4 + 7x^3 + 3x^2 - 2x) - (5x^4 + 4x^3 - 6x + 2) =

f) (x^2 + 14x - 6) - (3x^3 - 3x^2 + 10x + 5) =

g) (6x - 5x^4 + 4x^5 - 2x^7) - (-7x^5 + 5x - 2x^4 + 3x^2 - 5) =

h) (-3ab + 5a^2b + 4ab^2 - 6) - (4a^2b + 3ab^2 - 5 + 2ab) =

i) (x^2 + 30x + 225) - (4x^2 + 12x + 9) =

j) (x^3 + 3x^2 + 3x + 1) + (8x^3 + 12x^2 - 6x - 18) =

Accepted Answer

Let's solve each expression:

a) $(-2x^4 + 4x^3 + 6x^2 - 10x) + (x^4 + 2x^3 - 15x)$

Combine like terms:
$$
(-2x^4 + x^4) + (4x^3 + 2x^3) + 6x^2 + (-10x - 15x)
$$
$$
= -x^4 + 6x^3 + 6x^2 - 25x
$$

b) $(x^2 - 4x + 12) + (2x^3 - 4x + 20)$

Combine like terms:
$$
2x^3 + x^2 + (-4x - 4x) + (12 + 20)
$$
$$
= 2x^3 + x^2 - 8x + 32
$$

c) $(x^3 + 4x^2 - 6) + (2x^4 - x^5 + 3x^3)$

Combine like terms:
$$
(-x^5) + 2x^4 + (x^3 + 3x^3) + 4x^2 - 6
$$
$$
= -x^5 + 2x^4 + 4x^3 + 4x^2 - 6
$$

d) $(6x^5 - 2x^7 + 3x^3 - 5x + 2x^4) + (6x^5 - 3x^7 - 2x^6 + 4x^2 - 7)$

Combine like terms:
$$
(-2x^7 - 3x^7) + (6x^5 + 6x^5) + 2x^4 + 3x^3 + 4x^2 - 5x - 7
$$
$$
= -5x^7 + 12x^5 + 2x^4 + 3x^3 + 4x^2 - 5x - 7
$$

e) $(3x^4 + 7x^3 + 3x^2 - 2x) - (5x^4 + 4x^3 - 6x + 2)$

Combine like terms:
$$
(3x^4 - 5x^4) + (7x^3 - 4x^3) + 3x^2 + (-2x + 6x) - 2
$$
$$
= -2x^4 + 3x^3 + 3x^2 + 4x - 2
$$

f) $(x^2 + 14x - 6) - (3x^3 - 3x^2 + 10x + 5)$

Combine like terms:
$$
-3x^3 + (x^2 + 3x^2) + (14x - 10x) + (-6 - 5)
$$
$$
= -3x^3 + 4x^2 + 4x - 11
$$

g) $(6x - 5x^4 + 4x^5 - 2x^7) - (-7x^5 + 5x - 2x^4 + 3x^2 - 5)$

Combine like terms:
$$
(-2x^7) + (4x^5 + 7x^5) + (-5x^4 + 2x^4) + (6x - 5x) - 3x^2 + 5
$$
$$
= -2x^7 + 11x^5 - 3x^4 + x - 3x^2 + 5
$$

h) $(-3ab + 5a^2b + 4ab^2 - 6) - (4a^2b + 3ab^2 - 5 + 2ab)$

Combine like terms:
$$
(-3ab - 2ab) + (5a^2b - 4a^2b) + (4ab^2 - 3ab^2) + (-6 + 5)
$$
$$
= -5ab + a^2b + ab^2 - 1
$$

i) $(x^2 + 30x + 225) - (4x^2 + 12x + 9)$

Combine like terms:
$$
(x^2 - 4x^2) + (30x - 12x) + (225 - 9)
$$
$$
= -3x^2 + 18x + 216
$$

j) $(x^3 + x^2 + 3x + 1) + (8x^3 + 12x^2 - 6x - 18)$

Combine like terms:
$$
(x^3 + 8x^3) + (x^2 + 12x^2) + (3x - 6x) + (1 - 18)
$$
$$
= 9x^3 + 13x^2 - 3x - 17
$$

a) (-2x^4 + 4x^3 + 6x^2 - 10x) + (x^4 + 2x^3 - 15x) = b) (x...

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