Question

simplify the following polynomials. all final answers must be in standard form.

1. $(3y^{2}-4y + 1)+(-y^{2}+y - 2)$
2. $(2m^{2}-8m + 2)-(3m^{2}+5m + 7)$

Explanation:

Step1: Remove parentheses

$(3y^2 - 4y + 1) + (-y^2 + y - 2) = 3y^2 - 4y + 1 - y^2 + y - 2$

Step2: Combine like $y^2$ terms

$3y^2 - y^2 = 2y^2$

Step3: Combine like $y$ terms

$-4y + y = -3y$

Step4: Combine constant terms

$1 - 2 = -1$

Step5: Write in standard form

$2y^2 - 3y - 1$

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Step1: Distribute the negative sign

$(2m^2 - 8m + 2) - (3m^2 + 5m + 7) = 2m^2 - 8m + 2 - 3m^2 - 5m - 7$

Step2: Combine like $m^2$ terms

$2m^2 - 3m^2 = -m^2$

Step3: Combine like $m$ terms

$-8m - 5m = -13m$

Step4: Combine constant terms

$2 - 7 = -5$

Step5: Write in standard form

$-m^2 - 13m - 5$

Answer:

1. $2y^2 - 3y - 1$
2. $-m^2 - 13m - 5$