Question

subtract the following polynomials:
$(a^{3}-2a^{2})-(-4a^{3}+4a^{2})$
$5a^{3}-2a^{2}$
$-5a^{6}-5a^{4}$
$5a^{3}-6a^{2}$
$-2a^{3}-6a^{2}$

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial, we distribute the negative sign to each term inside the parentheses: \((a^3 - 2a^2) + 4a^3 - 4a^2\)

Step2: Combine like terms for \(a^3\)

Combine the terms with \(a^3\): \(a^3 + 4a^3 = 5a^3\)

Step3: Combine like terms for \(a^2\)

Combine the terms with \(a^2\): \(-2a^2 - 4a^2 = -6a^2\)

Step4: Write the final polynomial

Combine the results from Step 2 and Step 3: \(5a^3 - 6a^2\)

Answer:

\(5a^3 - 6a^2\) (corresponding to the option with this polynomial)