Question

perform the indicated operation.\\((4x^{3}-9x^{2}+10x - 3)-(3x^{3}-5x^{2}-7x + 2)\\)\\(\\)write the polynomial in standard form.\\((4x^{3}-9x^{2}+10x - 3)-(3x^{3}-5x^{2}-7x + 2)=\square\\)

Explanation:

Step1: Distribute the subtraction

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
\((4x^3 - 9x^2 + 10x - 3) - 3x^3 + 5x^2 + 7x - 2\)

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

Combine the \(x^3\) terms: \(4x^3 - 3x^3 = x^3\)

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

Combine the \(x^2\) terms: \(-9x^2 + 5x^2 = -4x^2\)

Step4: Combine like terms for \(x\)

Combine the \(x\) terms: \(10x + 7x = 17x\)

Step5: Combine constant terms

Combine the constant terms: \(-3 - 2 = -5\)

Answer:

\(x^3 - 4x^2 + 17x - 5\)