Sure, let's solve this polynomial subtraction step-by-step.
We are given two polynomials:
1. [tex]\( -8m^2 - 8m + 12 \)[/tex]
2. [tex]\( 2m^2 + 10m + 1 \)[/tex]
We need to subtract the second polynomial from the first polynomial.
Step 1: Write down the polynomials clearly:
[tex]\[ (-8m^2 - 8m + 12) \][/tex]
[tex]\[ (2m^2 + 10m + 1) \][/tex]
Step 2: Distribute the negative sign to each term in the second polynomial:
[tex]\[ - (2m^2 + 10m + 1) = -2m^2 - 10m - 1 \][/tex]
Step 3: Combine like terms from the first and the modified second polynomial:
[tex]\[ (-8m^2 - 8m + 12) + (-2m^2 - 10m - 1) \][/tex]
Step 4: Add the coefficients of each like term:
- For [tex]\(m^2\)[/tex]:
[tex]\[ -8m^2 - 2m^2 = -10m^2 \][/tex]
- For [tex]\(m\)[/tex]:
[tex]\[ -8m - 10m = -18m \][/tex]
- For the constant terms:
[tex]\[ 12 - 1 = 11 \][/tex]
Step 5: Combine these results to get the final polynomial:
[tex]\[ -10m^2 - 18m + 11 \][/tex]
So, the result of subtracting [tex]\((2m^2 + 10m + 1)\)[/tex] from [tex]\((-8m^2 - 8m + 12)\)[/tex] is:
[tex]\[ -10m^2 - 18m + 11 \][/tex]
