Question

1. find the result of subtracting $-3x^{2}+5x-7$ from $x^{2}-2x+1$

○ a. $-4x^{2}+7x-8$
○ b. $4x^{2}-7x+8$
○ c. $4x^{2}+3x-6$
○ d. $4x^{2}-7x-8$

1. simplify by adding $6x^{2}-x+3$ and $-2x^{2}+4x-5$

○ a. $4x^{2}+3x+2$
○ b. $4x^{2}+3x-2$
○ c. $8x^{2}+3x+8$
○ d. $4x^{2}+5x-2$

1. simplify by subtracting $5x-2$ from $3x+4$

○ a. $8x+2$
○ b. $-2x-6$
○ c. $-2x+6$
○ d. $2x+6$

Explanation:

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Problem 1:

Step1: Write subtraction expression

$(x^2 - 2x + 1) - (-3x^2 + 5x - 7)$

Step2: Distribute the negative sign

$x^2 - 2x + 1 + 3x^2 - 5x + 7$

Step3: Combine like terms

$(x^2+3x^2)+(-2x-5x)+(1+7) = 4x^2 -7x +8$
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Problem 2:

Step1: Write addition expression

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

Step2: Combine like terms

$(6x^2-2x^2)+(-x+4x)+(3-5) = 4x^2 +3x -2$
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Problem 3:

Step1: Write subtraction expression

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

Step2: Distribute the negative sign

$3x + 4 -5x + 2$

Step3: Combine like terms

$(3x-5x)+(4+2) = -2x +6$
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Answer:

1. b. $4x^2 -7x +8$
2. b. $4x^2 +3x -2$
3. c. $-2x +6$