Multiply -x – 2 by-x^2 + 4x – 2
To multiply the expressions (-x - 2) and (-x^2 + 4x - 2), we will use the distributive property. This property states that for any three numbers a, b, and c, (a+b) × c is equal to ac + bc. Applying this property, we will distribute each term of the first expression with every term of the second expression and then combine like terms if necessary.
Let's break down the multiplication step by step:
1. Multiply -x by each term in the second expression:
-x × -x^2 = x^3 (multiply the coefficients: -1 × -1 = 1, and add the exponents: x^1 × x^2 = x^3)
-x × 4x = -4x^2 (multiply the coefficients: -1 × 4 = -4, and add the exponents: x^1 × x^1 = x^2)
-x × -2 = 2x (multiply the coefficients: -1 × -2 = 2)
2. Multiply -2 by each term in the second expression:
-2 × -x^2 = 2x^2 (multiply the coefficients: -2 × -1 = 2)
-2 × 4x = -8x (multiply the coefficients: -2 × 4 = -8)
-2 × -2 = 4 (multiply the coefficients: -2 × -2 = 4)
3. Combine all the terms:
x^3 - 4x^2 + 2x + 2x^2 - 8x + 4
4. Simplify by combining like terms:
x^3 + (-4x^2 + 2x^2) + (2x - 8x) + 4
x^3 - 2x^2 - 6x + 4
Therefore, the product of (-x - 2) and (-x^2 + 4x - 2) is x^3 - 2x^2 - 6x + 4.