Grade 9 › G9U03 Polynomials

Grade 9 › G9U03 Polynomials › L4
GRADE 9 · ALBERTAOUTCOME AB-G9-9A1

L4 · Expanding products of two polynomials (each at most 3 terms)

Learning goal

“I can expand a product of two polynomials - binomial x binomial, binomial x trinomial, and squared binomials - by multiplying every term of one by every term of the other, using an area grid to keep the bookkeeping complete.”

Binomial — a polynomial with exactly two terms, e.g. x + 3 (review from L1).
Trinomial — a polynomial with exactly three terms, e.g. x^2 - 3x + 1 (review from L1).
Area grid — a rectangle split into rows and columns by the terms of the two factors; every cell is one product, so no product can be missed.
Identity — an expansion pattern that is always true, e.g. (a + b)^2 = a^2 + 2ab + b^2. Identities are shortcuts, not new rules.
Worked example

Expand (x + 3)(x + 2). Picture the area grid in words: a rectangle with width split into sections x and 3, and length split into sections x and 2. Four cells: x · x = x^2 (the big square tile); x · 2 = 2x; 3 · x = 3x; 3 · 2 = 6 (the unit tiles). Add the cells: x^2 + 2x + 3x + 6. The two x-terms are like terms, so combine: x^2 + 5x + 6. Say it plainly: a 2-term x 2-term product always makes four products before combining. If your working shows two, you have lost two cells.

Check yourself — explain it

Why does (x + 3)(x + 2) produce an x-term of 5x and not 6x or 2x?

Paired problem — example still visible

Expand (x + 4)(x - 1). -> x^2 + 3x - 4 (cells: x^2, -x, 4x, -4; combine -x + 4x = 3x)

Faded completion — last step is yours

"(x - 5)(x + 2) = x^2 - 3x - ___. What is the constant, and what is its sign?" -> 10, negative (the constant cell is -5 · 2 = -10)

Ready to practise?

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

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