(x^2+2x-8)(x-6)

2 min read Jun 17, 2024

Expanding the Expression: (x² + 2x - 8)(x - 6)

This expression involves multiplying two polynomials: a quadratic (x² + 2x - 8) and a linear (x - 6). We can expand this using the distributive property, also known as FOIL (First, Outer, Inner, Last).

Step 1: Distribute the first term of the quadratic

First: (x²)(x - 6) = x³ - 6x²
Outer: (2x)(x - 6) = 2x² - 12x
Inner: (-8)(x - 6) = -8x + 48

Step 2: Combine the terms

Now, combine all the terms we got from the distribution:

x³ - 6x² + 2x² - 12x - 8x + 48

Step 3: Simplify the expression

Finally, simplify by combining like terms:

x³ - 4x² - 20x + 48

Result

Therefore, the expanded form of (x² + 2x - 8)(x - 6) is x³ - 4x² - 20x + 48.

Key Points

FOIL: Remember the FOIL method for multiplying binomials.
Distributive Property: The distributive property is essential for expanding any polynomial multiplication.
Combining Like Terms: Always simplify the expression by combining terms with the same variable and exponent.