Question

in the given expression, calculate as indicated. express your answer as a single polynomial in stand
$(8x^3 - 7x^2 + 2x + 3) - (6x^2 - 5x + 5)$
$(8x^3 - 7x^2 + 2x + 3) - (6x^2 - 5x + 5) = \square$

Explanation:

Step1: Remove parentheses

To subtract the second polynomial from the first, we first remove the parentheses. When we remove the parentheses of the second polynomial, we have to distribute the negative sign to each term inside. So, \((8x^{3}-7x^{2}+2x + 3)-(6x^{2}-5x + 5)=8x^{3}-7x^{2}+2x + 3-6x^{2}+5x - 5\).

Step2: Combine like terms

• For the \(x^{3}\) term: We have only \(8x^{3}\), so it remains as \(8x^{3}\).
• For the \(x^{2}\) terms: We have \(-7x^{2}\) and \(-6x^{2}\). Combining them, we get \(-7x^{2}-6x^{2}=-13x^{2}\).
• For the \(x\) terms: We have \(2x\) and \(5x\). Combining them, we get \(2x + 5x=7x\).
• For the constant terms: We have \(3\) and \(-5\). Combining them, we get \(3-5=-2\).

Putting it all together, we have \(8x^{3}-13x^{2}+7x - 2\).

Answer:

\(8x^{3}-13x^{2}+7x - 2\)