We have looked at polynomials containing only one variable. However, a polynomial can contain several variables. All of the same rules apply when working with polynomials containing several variables. Consider an example:
(a+2b)(4a−b−c)a(4a−b−c)+2b(4a−b−c)Use the distributive property.4a2−ab−ac+8ab−2b2−2bcMultiply.4a2+(−ab+8ab)−ac−2b2−2bcCombine like terms.4a2+7ab−ac−2bc−2b2Simplify.
Example 8: Multiplying Polynomials Containing Several Variables
Multiply (x+4)(3x−2y+5).
Solution
Follow the same steps that we used to multiply polynomials containing only one variable.
x(3x−2y+5)+4(3x−2y+5)Use the distributive property.3x2−2xy+5x+12x−8y+20Multiply.3x2−2xy+(5x+12x)−8y+20Combine like terms.3x2−2xy+17x−8y+20Simplify.
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