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Subtract \([tex][tex]$11b^2 - 4b + 7$[/tex][/tex] from \([tex][tex]$b^2 + 8b - 9$[/tex][/tex].

Your answer should be a polynomial in standard form.
[tex]\square[/tex]


Sagot :

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.
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