Question

subtracting polynomial expressions
learning goal: i can subtract polynomials. (standard a-apr.a.1)
l41: math resources
https://bit.ly/l41-math
explore opposites of polynomials
read the section below and complete the following activity.
when you multiply a number by -1, you get the opposite, or additive inverse of that number. for example,
$-1(7) = -7$, $-1(-5) = 5$, $-1(0) = 0$, $-1(x) = -x$, $-1(-a) = a$
suppose you want to remove parentheses in an expression like $-1(4x^3 - 6y + 3)$. you must distribute the -1 to each term. the most efficient method is to simply replace each term in the parenthesis with its opposite (\change the sign of every term\).
opposites of polynomials
to find an equivalent polynomial for the opposite of a polynomial, change the sign of every term. this is the same as multiplying by -1.
examples find the opposite of each polynomial.
a. $-(4x^3 - 6x + 3)$
$-(4x^3 - 6x + 3) = -4x^3 + 6x - 3$ change the sign of every term
b. $-(-t^3 - 6t^2 - t + 4)$
$-(-t^3 - 6t^2 - t + 4) = t^3 + 6t^2 + t - 4$ change the sign of every term
find the opposite of each polynomial.

1. $-(a + b + c)$

$-(a + b + c) =$

1. $-(-x + 2y - z)$

$-(-x + 2y - z) =$

1. $-(-5m^2 - mn + n^2)$

$-(-5m^2 - mn + n^2) =$

Explanation:

Step1: Flip signs of all terms

$-(a + b + c) = -a - b - c$

Step2: Flip signs of all terms

$-(-x + 2y - z) = x - 2y + z$

Step3: Flip signs of all terms

$-(-5m^2 - mn + n^2) = 5m^2 + mn - n^2$

Answer:

1. $\boldsymbol{-a - b - c}$
2. $\boldsymbol{x - 2y + z}$
3. $\boldsymbol{5m^2 + mn - n^2}$