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Chapter 51: Multiplying and Dividing Polynomials
Distributive Property
Definition: A property used to multiply a term by each term inside parentheses.
Example: Simplifying the expression x²(x³ + 7y).
Step 1: Apply the distributive property: x² * (x³ + 7y) = (x² * x³) + (x² * 7y)
Step 2: Multiply exponents with the same base (add exponents): x² * x³ = x²+3 = x⁵.
Final simplified expression: x⁵ + 7x²y.
Note: x⁵ and 7x²y are NOT like terms.
Multiplying Monomials and Binomials
Example: Simplification of x²(x³ + 7y).
Calculation: x² * x³ = x⁵ and 7y * x² = 7x²y.
Result: x²(x³ + 7y) = x⁵ + 7x²y.
Example: Simplifying a³b(a²b¹ + ab²).
Use distributive property and combine like terms.
Result: a⁵b³.