Questions: Simplify the algebraic expression. 4(-2 x^2+2 x)-(2 x-5 x^2)

Transcript text: Simplify the algebraic expression. \[ 4\left(-2 x^{2}+2 x\right)-\left(2 x-5 x^{2}\right) \] $4\left(-2 x^{2}+2 x\right)-\left(2 x-5 x^{2}\right)=$ $\square$ (Simplify your answer. Do not factor.)

Solution

Solution Steps

Step 1: Expand the Expressions

Apply the distributive property to multiply 4 with each term inside the parentheses of the first polynomial expression, resulting in: \[4(-2x^2 + 2x) = -8x^2 + 8x\]

Step 2: Simplify the Subtraction

Subtract the terms of the second polynomial expression from the result of the first step, resulting in: \[-8x^2 + 8x - (2x - 5x^2) = -3x^2 + 6x\]

Step 3: Combine Like Terms

Since the terms are already separated by their degree, we directly use the simplified coefficients for x^2 and x terms.