Question

perform the operations and simplify. 3(x³ - 8x + 4) + 7(4x² + 3x) - 4

Explanation:

Step1: Distribute the coefficients

First, distribute the 3 into the first polynomial and the 7 into the second polynomial:
\(3(x^{3}-8x + 4)=3x^{3}-24x + 12\)
\(7(4x^{2}+3x)=28x^{2}+21x\)

Step2: Combine all terms

Now, combine all the terms from the distributed polynomials and the constant - 4:
\(3x^{3}-24x + 12+28x^{2}+21x-4\)

Step3: Combine like - terms

• For the \(x\) terms: \(-24x+21x=-3x\)
• For the constant terms: \(12 - 4 = 8\)

So, combining all the terms together: \(3x^{3}+28x^{2}-3x + 8\)

Answer:

\(3x^{3}+28x^{2}-3x + 8\)