Sure, let's work through the subtraction of these polynomials step by step.
We need to subtract the polynomial [tex]\( 11b^2 - 4b + 7 \)[/tex] from the polynomial [tex]\( b^2 + 8b - 9 \)[/tex].
Start by writing down both polynomials:
[tex]\[ \text{Polynomial 1: } b^2 + 8b - 9 \][/tex]
[tex]\[ \text{Polynomial 2: } 11b^2 - 4b + 7 \][/tex]
To subtract these, we'll subtract the corresponding coefficients of the polynomials.
Step 1: Subtract the coefficients of [tex]\( b^2 \)[/tex]:
[tex]\[ 1b^2 - 11b^2 = -10b^2 \][/tex]
Step 2: Subtract the coefficients of [tex]\( b \)[/tex]:
[tex]\[ 8b - (-4b) = 8b + 4b = 12b \][/tex]
Step 3: Subtract the constant terms:
[tex]\[ -9 - 7 = -16 \][/tex]
Now, combine the results from these steps to form the new polynomial:
[tex]\[ -10b^2 + 12b - 16 \][/tex]
So, the result of subtracting [tex]\( 11b^2 - 4b + 7 \)[/tex] from [tex]\( b^2 + 8b - 9 \)[/tex] is:
[tex]\[ -10b^2 + 12b - 16 \][/tex]
This is the polynomial in standard form.
