Subtract 11b^2-4b+7 from b^2+8b-9. Your answer should be a polynomial in standard form.

Write Problem: Write down the problem to be solved. We need to subtract $11b^2-4b+7$ from $b^2+8b-9$. This can be written as: $(b^2+8b-9) - (11b^2-4b+7)$Distribute Negative: Distribute the negative sign to the second polynomial. When we subtract polynomials, we need to distribute the negative sign to each term of the second polynomial. This changes the sign of each term in the second polynomial: $(b^2+8b-9) - 11b^2 + 4b - 7$Combine Like Terms: Combine like terms. Now we combine the terms with the same powers of $b$: $b^2 - 11b^2$ gives us $-10b^2$, $8b + 4b$ gives us $12b$, $-9 - 7$ gives us $-16$. So, the expression becomes: $-10b^2 + 12b - 16$Standard Form: Write the polynomial in standard form. The standard form for a polynomial is to write the terms in descending order of their degree. Our polynomial is already in standard form: $-10b^2 + 12b - 16$

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Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

Q. Subtract

11b^2-4b+7

from

b^2+8b-9.

\newline

Your answer should be a polynomial in standard form.

\newline

\square

Write Problem: Write down the problem to be solved. $\newline$ We need to subtract $11b^2-4b+7$ from $b^2+8b-9$ . This can be written as: $\newline$ $(b^2+8b-9) - (11b^2-4b+7)$
Distribute Negative: Distribute the negative sign to the second polynomial. $\newline$ When we subtract polynomials, we need to distribute the negative sign to each term of the second polynomial. This changes the sign of each term in the second polynomial: $\newline$ $(b^2+8b-9) - 11b^2 + 4b - 7$
Combine Like Terms: Combine like terms. $\newline$ Now we combine the terms with the same powers of $b$ : $\newline$ $b^2 - 11b^2$ gives us $-10b^2$ , $\newline$ $8b + 4b$ gives us $12b$ , $\newline$ $-9 - 7$ gives us $-16$ . $\newline$ So, the expression becomes: $\newline$ $-10b^2 + 12b - 16$
Standard Form: Write the polynomial in standard form. $\newline$ The standard form for a polynomial is to write the terms in descending order of their degree. Our polynomial is already in standard form: $\newline$ $-10b^2 + 12b - 16$