Grade 9 › G9U03 Polynomials

Grade 9 › G9U03 Polynomials › L3
GRADE 9 · ALBERTAOUTCOME AB-G9-9A1

L3 · Multiplying: monomials and polynomial x monomial

Learning goal

“I can multiply monomials using the exponent laws, and expand a monomial x polynomial product so that the monomial multiplies EVERY term - using an area model of algebra tiles to see why.”

Monomial — a single term: the product of a coefficient and a power, e.g. 3x^2, -5x, 7 (review from L1).
Distributive property — a(b + c) = ab + ac: the factor outside multiplies every term inside. It is the engine of all expanding in this unit.
Expand — rewrite a product as a sum of terms: the opposite direction from factoring (L5-L6).
Worked example

Multiply (3x^2)(-2x^3). Step 1: Separate the number parts from the variable parts: (3 · -2) and (x^2 · x^3). Step 2: Coefficients: 3 · -2 = -6. Powers: x^2 · x^3 = x^(2+3) = x^5 - the product-of-powers law, because x^2 · x^3 is (x·x)(x·x·x), five x's in a row. Step 3: Reassemble: -6x^5. Second example, same routine: (-4x)(5x^4) = (-4 · 5)(x · x^4) = -20x^5. Say it plainly: multiplication is the operation where exponents ADD. (Combining like terms in L2 never touched the exponents - keep the two moves separate in your head.)

Check yourself — explain it

In (3x^2)(-2x^3), why is the exponent 5 and not 6?

Paired problem — example still visible

Multiply (6x)(2x^2). -> 12x^3 (6 · 2 = 12; x · x^2 = x^3)

Faded completion — last step is yours

"(-5a^3)(___ a^2) = 10a^5. What is the missing coefficient?" -> -2 (-5 · -2 = 10; a^3 · a^2 = a^5)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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