Answered

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Subtract. Your answer should be a polynomial in standard form.

[tex]\[ \left(-5b^2 - 8b\right) - \left(-9b^3 - 5b^2 - 8b\right) = \][/tex]

[tex]\[ \square \][/tex]

Sagot :

GinnyAnswer
Sure, let's go through the subtraction step-by-step to arrive at the solution.

We start with the given expression:

[tex]\[ \left(-5 b^2 - 8 b\right) - \left(-9 b^3 - 5 b^2 - 8 b\right) \][/tex]

Step 1: Distribute the negative sign across the second polynomial expression to remove the parentheses.

[tex]\[ -5 b^2 - 8 b - (-9 b^3 - 5 b^2 - 8 b) \][/tex]

This simplifies to:

[tex]\[ -5 b^2 - 8 b + 9 b^3 + 5 b^2 + 8 b \][/tex]

Step 2: Combine like terms. Group together the terms with the same powers of [tex]\(b\)[/tex].

[tex]\[ (9 b^3) + (-5 b^2 + 5 b^2) + (-8 b + 8 b) \][/tex]

Step 3: Simplify each group of like terms.

For [tex]\(b^3\)[/tex] terms:
[tex]\[ 9 b^3 \][/tex]

For [tex]\(b^2\)[/tex] terms:
[tex]\[ -5 b^2 + 5 b^2 = 0 \][/tex]

For [tex]\(b\)[/tex] terms:
[tex]\[ -8 b + 8 b = 0 \][/tex]

So, the final result, after combining all the like terms, is:

[tex]\[ 9 b^3 \][/tex]

Therefore, the polynomial in standard form is:

[tex]\[ 9 b^3 \][/tex]
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