Question

what is the result of subtracting $(-2x^{4}+3x^{3}-x^{2}+x-5)$ from $(3x^{4}-x^{3}+2x^{2}-2x+1)$?
○ a. $x^{4}+2x^{3}-x^{2}+3x-6$
○ b. $5x^{4}-2x^{3}+3x^{2}-3x-4$
○ c. $5x^{4}-4x^{3}+x^{2}-3x+6$
○ d. $5x^{4}-4x^{3}+3x^{2}-3x+6$

simplify the expression by subtracting $4x^{2}-3x+2$ from $7x^{2}-4x+6$.
○ a. $11x^{2}-x+4$
○ b. $3x^{2}-x+8$
○ c. $3x^{2}-x+4$
○ d. $3x^{2}-7x+8$

find the result of adding $0.5x^{3}-1.2x^{2}+0.3x-2$ and $-0.5x^{3}+1.4x^{2}-0.3x+2$
○ a. $0.2x^{2}-4$
○ b. $0.2x^{2}+0$
○ c. $1.2x^{2}+0.3x$
○ d. $-1.1x^{3}+0.2x^{2}-2$

Explanation:

First Question

Step1: Write subtraction expression

$$(3x^4 - x^3 + 2x^2 - 2x + 1) - (-2x^4 + 3x^3 - x^2 + x - 5)$$

Step2: Distribute the negative sign

$$3x^4 - x^3 + 2x^2 - 2x + 1 + 2x^4 - 3x^3 + x^2 - x + 5$$

Step3: Combine like terms

• $x^4$ terms: $3x^4 + 2x^4 = 5x^4$
• $x^3$ terms: $-x^3 - 3x^3 = -4x^3$
• $x^2$ terms: $2x^2 + x^2 = 3x^2$
• $x$ terms: $-2x - x = -3x$
• constants: $1 + 5 = 6$

$$5x^4 - 4x^3 + 3x^2 - 3x + 6$$

Step1: Write subtraction expression

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

Step2: Distribute the negative sign

$$7x^2 - 4x + 6 - 4x^2 + 3x - 2$$

Step3: Combine like terms

• $x^2$ terms: $7x^2 - 4x^2 = 3x^2$
• $x$ terms: $-4x + 3x = -x$
• constants: $6 - 2 = 4$

$$3x^2 - x + 4$$

Step1: Write addition expression

$$(0.5x^3 - 1.2x^2 + 0.3x - 2) + (-0.5x^3 + 1.4x^2 - 0.3x + 2)$$

Step2: Combine like terms

• $x^3$ terms: $0.5x^3 - 0.5x^3 = 0$
• $x^2$ terms: $-1.2x^2 + 1.4x^2 = 0.2x^2$
• $x$ terms: $0.3x - 0.3x = 0$
• constants: $-2 + 2 = 0$

$$0.2x^2 + 0$$

Answer:

d. $5x^4 - 4x^3 + 3x^2 - 3x + 6$

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Second Question