(x-6)(x-7)-in-standard-form.jpeg "(x-5)(x-6)(x-7) In Standard Form")
Expanding (x-5)(x-6)(x-7) into Standard Form
This article will guide you through the process of expanding the expression (x-5)(x-6)(x-7) into standard form, which is a polynomial with terms arranged from highest to lowest degree.
Step 1: Multiply the first two factors
Begin by multiplying the first two factors, (x-5) and (x-6), using the FOIL method (First, Outer, Inner, Last):
(x-5)(x-6) = x² - 6x - 5x + 30
Simplify the expression by combining like terms:
x² - 11x + 30
Step 2: Multiply the result by the third factor
Now, multiply the result from step 1 (x² - 11x + 30) by the third factor (x-7):
(x² - 11x + 30)(x-7)
Use the distributive property to expand this product:
x²(x-7) - 11x(x-7) + 30(x-7)
Step 3: Distribute and simplify
Distribute each term and then combine like terms:
x³ - 7x² - 11x² + 77x + 30x - 210
Simplify by combining like terms:
x³ - 18x² + 107x - 210
Therefore, the standard form of the expanded expression (x-5)(x-6)(x-7) is x³ - 18x² + 107x - 210.