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subtract $a^4+4a^2b^2-2b^4$ from $-3^a+5a^2b^2+2b^4$ your answer should be a polynomial in standard form

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Change of base formula

Full solution

Q. subtract

a^4+4a^2b^2-2b^4

from

-3^a+5a^2b^2+2b^4

your answer should be a polynomial in standard form

Identify Polynomials: Identify the polynomials to be subtracted. $\newline$ First polynomial: $a^4 + 4a^2b^2 - 2b^4$ $\newline$ Second polynomial: $-3a^4 + 5a^2b^2 + 2b^4$ $\newline$ We need to subtract the first polynomial from the second polynomial.
Subtract Term by Term: Subtract the first polynomial from the second polynomial term by term. $\newline$ $(-3a^4 + 5a^2b^2 + 2b^4) - (a^4 + 4a^2b^2 - 2b^4)$ $\newline$ This is equivalent to: $\newline$ $-3a^4 - a^4 + 5a^2b^2 - 4a^2b^2 + 2b^4 - (-2b^4)$
Combine Like Terms: Combine like terms. $\newline$ $-3a^4 - a^4$ becomes $-4a^4$ $\newline$ $5a^2b^2 - 4a^2b^2$ becomes $a^2b^2$ $\newline$ $2b^4 - (-2b^4)$ becomes $2b^4 + 2b^4$ which simplifies to $4b^4$ $\newline$ So the resulting polynomial is: $\newline$ $-4a^4 + a^2b^2 + 4b^4$
Standard Form: Write the polynomial in standard form, which is in descending order of degree. $\newline$ The polynomial is already in standard form: $\newline$ $-4a^4 + a^2b^2 + 4b^4$

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