Question

what is the sum of the polynomials?
$(7x^3 - 4x^2) + (2x^3 - 4x^2)$
$\bigcirc$ $5x^3$
$\bigcirc$ $9x^3$
$\bigcirc$ $5x^3 - 8x^2$
$\bigcirc$ $9x^3 - 8x^2$

Explanation:

Step1: Combine like terms for \(x^3\)

To find the sum of the polynomials \((7x^3 - 4x^2)+(2x^3 - 4x^2)\), we first combine the terms with \(x^3\). The coefficients of \(x^3\) are \(7\) and \(2\). So, \(7x^3+2x^3=(7 + 2)x^3 = 9x^3\).

Step2: Combine like terms for \(x^2\)

Next, we combine the terms with \(x^2\). The coefficients of \(x^2\) are \(- 4\) and \(-4\). So, \(-4x^2-4x^2=(-4-4)x^2=-8x^2\).

Step3: Combine the results

Combining the results from Step 1 and Step 2, we get \(9x^3-8x^2\).

Answer:

D. \(9x^3 - 8x^2\) (assuming the options are labeled A to D as per standard multiple - choice, with D being \(9x^3 - 8x^2\))